{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gauss Newton Algorithm \n",
    "\n",
    "The Gauss–Newton algorithm is used to solve non-linear least squares problems. It is a modification of Newton's method for finding a minimum of a function. Unlike Newton's method, the Gauss–Newton algorithm can only be used to minimize a sum of squared function values, but it has the advantage that second derivatives, which can be challenging to compute, are not required.\n",
    "\n",
    "Non-linear least squares problems arise for instance in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations.\n",
    "\n",
    "We use Gauss-Newton algorithm to minimize the cost function. The cost function in our case is the difference between the known 'gravitational and earth's magnetic vectors' and the (sensors accelerometer and magnetometer) readings transformed to the Earth frame. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the data from the sensors for acceleration and magnetic vectors as observation vectors. They are symbolized as \n",
    "\n",
    "\\begin{equation}\n",
    "A_{Device} = (a_{xb}, a_{yb}, a_{zb})\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "M_{Device} = (m_{xb}, m_{yb}, m_{zb})\n",
    "\\end{equation}\n",
    "\n",
    "In the Earth's frame of reference, the acceleration and magnetic vector represetation is \n",
    "\\begin{equation}\n",
    "A_{Earth} = (0, g, 0)\n",
    "\\end{equation}\n",
    "\n",
    "Where, $g$ is Earth's gravitational acceleration equal to $9.8 m/s^2$\n",
    "\\begin{equation}\n",
    "M_{Earth} = (m_{xE}, m_{yE}, m_{zE})\n",
    "\\end{equation}\n",
    "\n",
    "By combining the vecotrs in each of the references we get \n",
    "\\begin{equation}\n",
    "Y_{Earth} = (0, g, 0, m_{xE}, m_{yE}, m_{zE})\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "Y_{device} = (a_{xb}, a_{yb}, a_{zb}, m_{xb}, m_{yb}, m_{zb})\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rotation matrix that shall rotate the device vector to the Earth vector, in quaternion form is : \n",
    "\n",
    "\n",
    "$$\\mathbf{R_{t}} = \\left[\\begin{array}\n",
    "{rrr}\n",
    "M_{t} & 0 \\\\\n",
    "0 & M_{t} \n",
    "\\end{array}\\right]\n",
    "$$\n",
    "\n",
    "Where the matrix M is described as : \n",
    "$$\\mathbf{M_{t}} = \\left[\\begin{array}\n",
    "{rrr}\n",
    "q_4^2+q_1^2-q_2^2-q_3^2 & 2(q_1q_2-q_3q_4) & 2(q_1q_3 + q_2q_4) \\\\\n",
    "2(q_1q_2 + q_3q_4) & q_4^2+q_2^2-q_1^2-q_3^2 & 2(q_2q_3-q_4q_1)\\\\\n",
    "2(q_1q_3 - q_2q_4) & 2(q_3q_2+q_1q_4) & q_4^2+q_3^2-q_1^2-q_2^2)\n",
    "\\end{array}\\right]\n",
    "$$\n",
    "\n",
    "The Gauss-Newton optimization method is used to minimize discrepancy between\n",
    "actual and computed measurement vectors as below equation : \n",
    "\n",
    "\\begin{equation}\n",
    "\\epsilon  = Y_{Earth} - R_{t}.Y_{Device}\n",
    "\\end{equation}\n",
    "\n",
    "The Gauss-Newton method executes following iteration:\n",
    "\n",
    "\\begin{equation}\n",
    " q_t = q_{t-1} - (J_{t}^T.J_{t})^{-1}.J_{t}^T.\\epsilon\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "Where $J_k$ is the Jacobian of $\\epsilon$ calculated in $q_k$ as is shown in below equation\n",
    "\\begin{equation}\n",
    " J_{t}(q_{k}(t)) = \\frac{\\partial \\epsilon}{\\partial (q_{k}(t))} = - [ (\\frac{\\partial R}{\\partial (q_{1})} . Y_{Device(t)})(\\frac{\\partial R}{\\partial (q_{2})} . Y_{Device(t)})((\\frac{\\partial R}{\\partial (q_{3})} . Y_{Device(t)}))((\\frac{\\partial R}{\\partial (q_{4})} . Y_{Device(t)}))  ]  \n",
    "\\end{equation}\n",
    " \n",
    "and solving Jacobian.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a class for Gauss Newton Algorithm\n",
    "\n",
    "**class GaussNewtonOptimization **\n",
    "\n",
    "With **methods** for \n",
    "    1. normalize : norm\n",
    "    2. Gaussnewton operation : Gaussnewton"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We collected data with **No Rotation**, i.e 0,0,0 at X,Y,Z and that was measured on the device using **'Orientation Sensor'** readings, which is part of the application. So we collect the outcome at each iteration of the Gauss Newton algorithm, and look for convergence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from numpy import linalg as la\n",
    "\n",
    "class GaussNewtonOptimization:\n",
    "    \"\"\"\n",
    "    The Gauss–Newton algorithm is used to solve non-linear least squares problems. \n",
    "    \"\"\"\n",
    "    ## class variables : to be used later \n",
    "    counter = 0\n",
    "    depth = 50\n",
    "    \n",
    "    def __call__(self):\n",
    "        GaussNewtonOptimization.counter += 1\n",
    "        return GaussNewtonOptimization.counter\n",
    "    \n",
    "    def __init__(self, Q1,Q2,Q3,Q4,Ax,Ay,Az,Mx,My,Mz):\n",
    "        self.Q1 = Q1\n",
    "        self.Q2 = Q2\n",
    "        self.Q3 = Q3\n",
    "        self.Q4 = Q4\n",
    "        \n",
    "        self.Ax = Ax\n",
    "        self.Ay = Ay\n",
    "        self.Az = Az\n",
    "        \n",
    "        self.Mx = Mx\n",
    "        self.My = My\n",
    "        self.Mz = Mz\n",
    "        \n",
    "        ## added changes considering equation 4.67 from page 60\n",
    "        self.Q_now = list([self.Q1,self.Q2,self.Q3,self.Q4])\n",
    "\n",
    "    \n",
    "    def norm(Q):\n",
    "        \"\"\"\n",
    "        return the norm of the Quaternion.\n",
    "        \"\"\"\n",
    "        return sum( i*i for i in Q)\n",
    "\n",
    "    def Gaussnewton(self):\n",
    "        \"\"\"\n",
    "        Gauss Newton Algorithm : returns the Quaternion derived from Accelerometer and Magnetometer,\n",
    "        iterated 10 times. \n",
    "        \"\"\"\n",
    "        Q1 = self.Q1\n",
    "        Q2 = self.Q2 \n",
    "        Q3 = self.Q3 \n",
    "        Q4 = self.Q4 \n",
    "        \n",
    "        Ax = self.Ax \n",
    "        Ay = self.Ay \n",
    "        Az = self.Az \n",
    "        \n",
    "        Mx = self.Mx \n",
    "        My = self.My\n",
    "        Mz = self.Mz \n",
    "        \n",
    "        # reference Attitude\n",
    "#Ax           4.030215e-01\n",
    "#Ay          -1.938762e-01\n",
    "#Az           9.632899e+00\n",
    "#MFx         -2.680208e+00\n",
    "#MFy          2.209064e+01\n",
    "#MFz         -3.946090e+01\n",
    "\n",
    "## at 50 degrees at X\n",
    "#Timestamp    1.494780e+12\n",
    "#Ax           3.498182e-01\n",
    "#Ay          -1.278746e-01\n",
    "#Az           9.645478e+00\n",
    "#MFx         -8.154090e+00\n",
    "#MFy          6.280098e+00\n",
    "#MFz         -3.016979e+01\n",
    "#dtype: float64\n",
    "    \n",
    "\n",
    "        #EarthFrame = np.matrix([[0], [1] , [0], [0], [-0.03751], [0.92696]])\n",
    "        EarthFrame = np.matrix([[0.403], [-0.19380] , [-9.63], [-2.680208], [22.09064], [-39.46090]])\n",
    "        BodyFrame = np.matrix([[Ax], [Ay] , [Az], [Mx], [My], [Mz]])\n",
    "        \n",
    "        \n",
    "        Q_now = list([Q1,Q2,Q3,Q4])\n",
    "        #self.Q_now\n",
    "        #normalize\n",
    "        Q_now = [x / GaussNewtonOptimization.norm(Q_now) for x in Q_now]   \n",
    "               \n",
    "        q1 = Q_now[0] ; q2 = Q_now[1] ; q3 = Q_now[2] ; q4 = Q_now[3] \n",
    "        #from list to a column matrix\n",
    "        Q_now = np.matrix(Q_now).transpose()\n",
    "        #temp = Q_now\n",
    "        intermediateQ = list()\n",
    "        intermediateQ.append(Q_now)\n",
    "        \n",
    "        \n",
    "        for i in range(0,GaussNewtonOptimization.depth):\n",
    "            ## Compute Mt matrix\n",
    "\n",
    "            # The rotation matrix that rotates the \"body vector\" to the \"Earth vector\", in Quaternion form, \n",
    "            # is expressed in equation XX of the article; which has Mt matrix in it. \n",
    "\n",
    "            ## elements of Mt matrix \n",
    "            mm11 = (q4**2+q1**2-q2**2-q3**2)  ;   mm12 = 2*(q1*q2-q3*q4)           ;  mm13 = 2*(q1*q3+q2*q4)\n",
    "            mm21 = 2*(q1*q2+q3*q4)            ;   mm22 = (q4**2+q2**2-q1**2-q3**2) ;  mm23 = 2*(q2*q3-q4*q1)\n",
    "            mm31 = 2*(q1*q3-q2*q4)            ;   mm32 = 2*(q3*q2+q1*q4)           ;  mm33 = (q4**2+q3**2-q1**2-q2**2)  \n",
    "\n",
    "            Mt = np.matrix([[mm11, mm12, mm13], [mm21, mm22, mm23] , [mm31, mm32, mm33]])\n",
    "            zero33 = np.matrix(np.zeros((3,3)))  \n",
    "\n",
    "            ## Rotation Matrix (6 * 6)\n",
    "            Rt = np.hstack((np.vstack((Mt,zero33)),np.vstack((zero33,Mt))))\n",
    "\n",
    "            ## Jacobian Computation \n",
    "\n",
    "            j11 = 2*(q1*Ax + q2*Ay + q3*Az)\n",
    "            j12 = 2*(-q2*Ax +  q1*Ay + q4*Az) \n",
    "            j13 = 2*(q3*Ax - q4*Ay + q1*Az)\n",
    "            j14 = 2*(q4*Ax - q3*Ay + q2*Az)\n",
    "\n",
    "            j21 = 2*(q2*Ax - q1*Ay - q4*Az)\n",
    "            j22 = 2*(q1*Ax - q1*Ay - q4*Az)\n",
    "            j23 = 2*(q4*Ax - q3*Ay + q2*Az)\n",
    "            j24 = 2*(q3*Ax + q4*Ay - q1*Az)\n",
    "\n",
    "            j31 = 2*(q3*Ax + q4*Ay - q1*Az)\n",
    "            j32 = 2*(-q4*Ax + q3*Ay - q2*Az)\n",
    "            j33 = 2*(q1*Ax + q2*Ay + q3*Az)\n",
    "            j34 = 2*(q2*Ax + q1*Ay + q4*Az)\n",
    "\n",
    "            j41 = 2*(q1*Mx + q2*My + q3*Mz)\n",
    "            j42 = 2*(-q2*Mx + q1*My + q4*Mz)\n",
    "            j43 = 2*(-q3*Mx - q4*My + q1*Mz)\n",
    "            j44 = 2*(q4*Mx - q3*My + q2*Mz)\n",
    "\n",
    "            j51 = 2*(q2*Mx - q1*My - q4*Mz)\n",
    "            j52 = 2*(q1*Mx + q2*My + q3*Mz)\n",
    "            j53 = 2*(q4*Mx - q3*My + q2*Mz)\n",
    "            j54 = 2*(q3*Mx + q4*My - q1*Mz)\n",
    "\n",
    "            j61 = 2*(q3*Mx + q4*My - q1*Mz)\n",
    "            j62 = 2*(-q4*Mx + q3*My - q2*Mz)\n",
    "            j63 = 2*(q1*Mx + q2*My + q3*Mz)\n",
    "            j64 = 2*(-q2*Mx + q1*My + q4*Mz)\n",
    "\n",
    "            Mt = np.matrix([[mm11, mm12, mm13], [mm21, mm22, mm23] , [mm31, mm32, mm33]])\n",
    "            Jacobian_matrix = -np.matrix([[j11,j12,j13,j14],\n",
    "                                         [j21,j22,j23,j24],\n",
    "                                         [j31,j32,j33,j34],\n",
    "                                         [j41,j42,j43,j44],\n",
    "                                         [j51,j52,j53,j54],\n",
    "                                         [j61,j62,j63,j64],                                  \n",
    "                                        ])\n",
    "\n",
    "            f = EarthFrame - (Rt * BodyFrame)\n",
    "            \n",
    "            \n",
    "            ## Gauss Newton\n",
    "            Q_next = Q_now - (la.inv(Jacobian_matrix.transpose()*Jacobian_matrix ) ) * (Jacobian_matrix.transpose() * f)\n",
    "            \n",
    "            #normalize (do not renormalise in Kalman filter)\n",
    "            Q_next = [x / GaussNewtonOptimization.norm(np.array(Q_next).flatten()) for x in np.array(Q_next).flatten()]  \n",
    "            \n",
    "            \n",
    "            \n",
    "            # update quaternions\n",
    "            q1 = Q_next[0] ; q2 = Q_next[1] ; q3 = Q_next[2] ; q4 = Q_next[3] \n",
    "            Q_now = np.matrix(Q_next).transpose()\n",
    "            intermediateQ.append(Q_now)\n",
    "            #End of 'for' loop\n",
    "            \n",
    "        q1 = Q_next[0] ; q2 = Q_next[1] ; q3 = Q_next[2] ; q4 = Q_next[3]\n",
    "        return intermediateQ\n",
    "        #return q1,q2,q3,q4\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Execute the Gauss Newton Algorithm\n",
    "\n",
    "### Import the data \n",
    "\n",
    "We import the data from a text file, and save it as a Pandas dataframe. Add column Names to it. \n",
    "\n",
    "1. Accelerometer  : $A_{x},A_{y},A_{z}$ \n",
    "2. Magnetometer   : $MF_x,MF_y,MF_z$\n",
    "\n",
    "will be the columns of interest for us.     \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Timestamp        Ax        Ay        Az        Gx        Gy  \\\n",
      "1125  1494275017864  0.402226 -0.210690  9.595961 -0.004261  0.002131   \n",
      "1126  1494275017886  0.383072 -0.191536  9.672575 -0.004261  0.002131   \n",
      "1127  1494275017909  0.402226 -0.191536  9.576807  0.002131  0.003196   \n",
      "1128  1494275017930  0.383072 -0.191536  9.672575 -0.003196  0.001065   \n",
      "1129  1494275017952  0.421380 -0.191536  9.615114 -0.004261 -0.001065   \n",
      "\n",
      "            Gz   MFx    MFy    MFz  \n",
      "1125  0.002131 -2.75  22.25 -39.75  \n",
      "1126  0.002131 -2.25  21.75 -39.25  \n",
      "1127  0.001065 -2.25  21.75 -39.25  \n",
      "1128  0.001065 -1.75  21.75 -39.00  \n",
      "1129  0.004261 -1.75  21.75 -39.00  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Timestamp    1.494275e+12\n",
       "Ax           4.030215e-01\n",
       "Ay          -1.938762e-01\n",
       "Az           9.632899e+00\n",
       "Gx          -1.060709e-03\n",
       "Gy           3.092325e-03\n",
       "Gz           1.810039e-03\n",
       "MFx         -2.680208e+00\n",
       "MFy          2.209064e+01\n",
       "MFz         -3.946090e+01\n",
       "dtype: float64"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import Libraries \n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "# set the plot frame\n",
    "%matplotlib inline\n",
    "matplotlib.rcParams['figure.figsize'] = (20.0, 10.0)\n",
    "\n",
    "# import data\n",
    "#AtX50degrees\n",
    "#At0degrees\n",
    "dataraw = pd.read_csv(\"/home/omkar/thesis/Version4/rawdata/At0degrees.txt\", skiprows=4)\n",
    "## Data Extraction\n",
    "dataraw.columns = ['Timestamp','STK3310_Proximity_sensor_x','STK3310_Proximity_sensor_y','STK3310_Proximity_sensor_z', \n",
    "             'STK3310_Light_sensor_x','STK3310_Light_sensor_y','STK3310_Light_sensor_z',\n",
    "             'Display_Rotation_sensor_x','Display_Rotation_sensor_y','Display_Rotation_sensor_z',\n",
    "             'Ax','Ay','Az',\n",
    "             'MFx','MFy','MFz', \n",
    "             'Gx','Gy','Gz',\n",
    "             'Rotation_Vector_Sensor_x','Rotation_Vector_Sensor_y','Rotation_Vector_Sensor_z',\n",
    "             'Gravity_Sensor_x','Gravity_Sensor_y','Gravity_Sensor_z',\n",
    "             'Linear_Acceleration_Sensor_x','Linear_Acceleration_Sensor_y','Linear_Acceleration_Sensor_z',\n",
    "             'Orientation_Sensor_x','Orientation_Sensor_y','Orientation_Sensor_z']\n",
    "data = dataraw[['Timestamp','Ax','Ay','Az','Gx','Gy','Gz','MFx','MFy','MFz']]\n",
    "print(data[1125:1130])\n",
    "(data.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values considered are     \n",
    "$A_{x}=0.402226, \\ A_{y}=-0.210690,\\ A_{z}=9.595961$     \n",
    "$MF_x=-2.75,\\ MF_y=22.25,\\ MF_z=-39.75$    \n",
    "\n",
    "For the 0,0,0 orientation, which is the observation 1125th row. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f47cbe6ef98>"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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n0tDcQHVTte83bHN6zyElMoX+Sf1ZVbyKfkn9GJk2kvOyz6PWWUtUSBQze8xk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\nwwZqhmEYhmEYhmEY04z/DzyNMvWr+OGIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f47cbb62e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PPJBAIMBDDz20eZjP59v8ecqUKVx88cWMHTuWgoKCdk//99BpixBCCCGEEKKjyP/wdSql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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f47cbcd9198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uN0Taxws/kLZx5WvSWQisJ6OGvqpqYzudLPVLcIjUmY1ayzFlRst7d++Wtqeq\npCRIvdjTZwQkO+7QSQ63DiOkI7Z3kQQuvafAb88cfJ2wU/0Tku6y4Hu9qnLPHvn+7usLsPkjqfsq\nBngte3q3W785FPpMtw+sCw/GS71fXirt+7Yv4Of7vctMflEy/e5tXDEPFj/uDczcZd432QJSF5YV\ny6iDu8MHMsrfzWnDlzwjo9ZDr4XsA7D2bXm/aSdpT7/9tzPlfr//TJWWVYzQNWot23aPflorwcXC\n/5P68ML3ZV+/PumcwwgJtMqK5Zlhd0e8/4VSBiN+ljo1cStg5D53t2N1gqUue7ZD5eP4x08SKK17\nV+7RBi1kSjxA43beOvK3Z2T21Uk3S91XXipt/ccXeBNlrftLHbbqDTnHvpp3k85zv/MkuVKcJ3W5\newYFQOQi+Q2BtifI/VdR17Fyv1z2mQRW+xZLf6Riu1Gd+6Jk9NadSK0XIuc0K1aOPd6Z5tp+mPRD\nmrSTOuDtUdIOpUfKQEHLnjKjwO3aH2Hpc/6JKV9DrpGE9ZzL5d5u3gUuniVlwD2a6daylyR+K47E\ngiQRB14i99H2ud7+hmfdntJutewhgeSU12S0ODBIRlZ96y7fRD5In65BCxj7kCRg3P69zn92ilvT\nTt7+8tiHZVRt1evSBjQLk9HZ8mLvCPOCh/2vab/zpS/SZYzUr1//S+47V5nUn7dvlrowJ8E7IgnS\n53SXT5DBBPcsA/AmgKrjTnzXqS+vQzpgbt9YS4O5wSfYDc9OlgY4JVwagz5ny4f56dIZat4VTr6l\n6g3sXyod5dxEb0bKPc0RpFObEg6DroD3xnnXeyhBhq/dXC6pIMqKYPxj3koNZIh14cOw2cla3Bcl\nhXfXN9KZHnyVRPAgWcPNH0uGpEW3g3/5DR9KB7LXZLisihFC32j+olnQ71z5O2M//PKYN2gEuG1T\n5f25XPBEM+kAPuQ0FLFrJJs99v+kEbJWGoVGrWCEE0iU5Mt7J1xa/VSjDR9KRbDyVSmwU9+QirT7\nBLiywjNiM8bJeTnjWbmO0Stg62eSactLlqkbPSZWuRuPlHDpFJ72oDT6h2vLp/JcE8jIwLB/Vr3c\nO6O9o7z3R3mDtvXvy1zpIddCh6FVr+tmrYySFGVJ8Ju+V6bjueeWX/O9d+owyGhdWaEcU346vNBV\n3r9pRdXnf/nLErT1PqvyZxW/c+xqGHy1TOf1PbbkHd7y49tBcCvK8U6LBMkUTnnV+zo/TX71q+J0\n1iFXy71IXkSnAAAgAElEQVTgnkYGMiVo5K2SpPAVuUiOoecZMrpccZpPq75w429yj7tHfPtfIMma\n0fd6p9z42verdDrKS2V7XUbL1CNj5OF2d2D1z4XSiE0f5t/xu3WjTHkqyobfnpPvE7lAGoS+Uyvv\n71CSdjidLAsYqXPG/Z+3XG2aLQ0bSJ0z6m4Z5bYW/utM0bh0jowCmABnGlpv7/Y3fCAjwG5ho/yn\n07ivd/shsr67ATWB8IgTsG7+CDoMl7Iy9qHKUxkrcl/7gDoScG2aJR2OGxZXvXxukgQWLbpLEOz2\naGbl6XcfXyhBbkVjH/aOOo5/1H9E2FUuAZoth3GPQqCTpCnIkOPsMbH6+sXlkjYmZqV0Ok66Re4t\nkDLw69OSOCtIk87Jv9d5y517amKDFjJV0xh4qY93imlFQ66RgM73Gq1/X8pEVVOgdsyTsuFbXira\n+pnUp8Eh0m7VqVt5mdJCWPykJErqNpDAadDlklnOiJJyMfw676hNfrrMiMiMkbIP0jk6y5mqv2m2\n1GkmQDr8rvLK5RokyfVkC58DMch94AisJ+WyRXeZZuxbBxVmSYd06LWSFHRPQ3eb+iYMrvAjTQUZ\n3sRYw1BJLqyaLjM1Vr0u9XrzbnB7NSOfID/4404AnHyrJMa+uFoC2Cmvy3l2J1mqqjc99WKhk6l/\nRDqpz3aQZOFd2/3v7Tu2+T/yYQLg/1K9ZRik7dw4U7Y3/lH/volbWbE8NuEqlaB60OXezxI2S/sT\nECTBj7t8H4mNM+UYh1zt//6GD2VE2betOZTtcyVpUZgh7ciQa2SaoMslbU+Jz/NNU16X8vnuGO97\nt2+WvmFNbP7EmxBuPxSG/ePgy/sqLYL/DZf2JKihPDLSrIuMAFfVBs25rOoZAx2GS90auVCCgCFX\nSyC57QsJpMY+JAHm3H96k/W+U37dPpjk/S5Xf+ttVxO2+J+fjidJ/6HfuTISvG6GTE30HSF1l3G3\nA+tkVs+ou6RP7jZ9qNzzbu7HW9wKMqTP6H584aaVkuQ8GHcyt+ckuV+7T5Dz0fYEGHqNd7vue3ro\ntTLK+XRreT3yNuhymgS9Ay+Re9wESh+xYYuq9uivMAue6yx/P14h+RO7VtrFgDqyH9++9XbnWcEe\np0vfZfETkqBY8Yq0Iam7/ZNAAK0HSH2x+3u5H8tLJEgOGyXJi71O29l9PKb/+bU0mBs2zG7YcBR+\nVaysWEZqEjZXHdiAFLalz0m29Ly3D38f0SvlZvTN3vwe1src7HaDoUnbqpfJ2C//dZ9Q+bOsA5J9\naRgqhaoqB9ZJFudQN9aRmjHem0ECGYms2HHKjJbnKbqPPzbHUFMRCyRAONgzFim75ft0PMn7HMPR\nkrZXsq9dxxx8udwkacB9nxE4FpJ2SIXTd6o0IhXt/w1COsqUos6n1KyC9BWxUDq6hwp+QRII4d9L\nZ6lxG5nD3uds6SSWl0nQ17rf7+uI/HCPdGrGPSLBIEjw99F58rd7VOzPIm6DNDg9qrj3j0R5mWQ5\nY1ZIo3hSDaf7Hmqbu+dLltr3+YDq7F0kdXXDUG8CzNeen+QHmEBGPs56WUbCep3p/NDBPpkqdCzv\ni4qKsmVEr9s4/yl9OQlSfkL7eMt4WqQkqL681ttpajtIOgR9p1bdEf8z27tIyuCRHvt3t0nwd+U8\naHOCjIL2PFM6NV1Ge0fpDyV9n4xUFqTLtNIuo6tebubZMjXtrp3+nVGXM2Mm7NRD12Ope2TkrO+5\nElRlx8mUuT5nO7MjMmQfvc+uut6sStQyGVlytynxG6Xj2W6QPG9YkCGBePuhMspwJDJjpL3vM0VG\n02uzA+u8neG2J0hQUpgpP/ADkowe858/7ngKs6T/0H28d2S+OqumS/Lh3LelX1envjz732eKlF/f\nslSV7HhJOjZoWfWzfu6grW4jea7VPSjh/jEw94hz2KnyDL+vTy+VxOCw6yRw7nFGzdr11Ah5Rh0k\n8V/d/Ze0Xfp7vc8+dB2dFSvXuKq+ra99v8rIaZ8pss2oZfIDLe778/fIiJIE26EGXmrizZEysm8C\nJdEQ70zxjt8kx17D+tMY88cFc8aYjsBsoDWSanvXWvuaMaY58DkQBkQDF1trM6vbDhzFYA4kQ1iQ\n7p3WWJWcRMmCVPVAtjp8ZSXwlNPBqTh6o9SfSXmZjJqEdPRvaJ7v6nQSK4yY/hW5yiXIaNzmeB9J\n9XKTZYQhuKn8QEJtVJjlTPXPk85fTTv9fzXWSnKqumTl4SgrkamMB+t8lhTIKE9Ng0RVuyx/SWay\nXLfwz3uNrZWEzrGsY92/rn2456C0SNq6kPZH/5j+7opzpe0KbnLwGOQQ/uhgri3Q1lq7yRjTGNgI\nnAtcC2RYa6cZYx4AmllrD5rqPqrBnDo+ngyVYeObVx+9UUul/ijRK2HLJ/IsnO/Ua6WUUkqpP8jh\nBHO/c1wSrLWJQKLzd64xJhxoD0wFTnMWmwX8BvyJ5i2pY+Lqb+XZGQ3kVG0Udor8p5RSSilVC/zu\nYM6XMSYMGAysBVo7gR5AEjINs6p1bgRuBOjU6Qjnh6s/j84jj/cRKKWUUkop9bdw1B4WM8Y0AuYB\nd1prc3w/szKXs8r5nNbad621w6y1w0JDQ6taRCmllFJKKaVUBUclmDPGBCGB3CfW2q+ct5Od5+nc\nz9WlVLe+UkoppZRSSqnD87uDOWOMAd4Hwq21Pv8MOt8B7n/p9hqgmn9dVCmllFJKKaXU4Toaz8yd\nAlwFbDfGbHHeewiYBnxhjLkOiAEurmZ9pZRSSimllFKH6Wj8muUKoLp/EfA4/8vQSimllFJKKfXX\npP9atlJKKaWUUkrVQhrMKaWUUkoppVQtpMGcUkoppZRSStVCGswppZRSSimlVC2kwZxSSimllFJK\n1UIazCmllFJKKaVULaTBnFJKKaWUUkrVQhrMKaWUUkoppVQtpMGcUkoppZRSStVCGswppZRSSiml\nVC2kwZxSSimllFJK1UIazCmllFJKKaVULaTBnFJKKaWUUkrVQhrMKaWUUkoppVQtpMGcUkoppZRS\nStVCGswppZRSSimlVC2kwZxSSimllFJK1UIazCmllFJKKaVULaTBnFJKKaWUUkrVQhrMKaWUUkop\npVQtpMGcUkoppZRSStVCGswppZRSSimlVC10VII5Y8wHxpgUY8wOn/eaG2N+McZEOv9vdjT2pZRS\nSimllFLq6I3MzQQmVXjvAWCxtbYHsNh5rZRSSimllFLqKDgqwZy1dhmQUeHtqcAs5+9ZwLlHY19K\nKaWUUkoppY7tM3OtrbWJzt9JQOuqFjLG3GiM2WCM2ZCamnoMD0cppZRSSiml/jr+kB9AsdZawFbz\n2bvW2mHW2mGhoaF/xOEopZRSSimlVK13LIO5ZGNMWwDn/ynHcF9KKaWUUkop9bdyLIO574BrnL+v\nAb49hvtSSimllFJKqb+Vo/VPE8wBVgO9jDFxxpjrgGnARGNMJDDBea2UUkoppZRS6iioczQ2Yq29\nrJqPxh+N7SullFJKKaWU8veH/ACKUkoppZRSSqmjS4M5pZRSSimllKqFNJhTSimllFJKqVpIgzml\nlFJKKaWUqoU0mFNKKaWUUkqpWkiDOaWUUkoppZSqhTSYU0oppZRSSqlaSIM5pZRSSimllKqFNJhT\nSimllFJKqVpIgzmllFJKKaWUqoU0mFNKKaWUUkqpWkiDOaWUUkoppZSqhTSYU0oppZRSSqlaSIM5\npZRSSimllKqFNJhTSimllFJKqVpIgzmllFJKKaWUqoU0mFNKKaWUUkqpWkiDOaWUUkoppZSqhTSY\nU0oppZRSSqlaSIM5pZRSSimllKqFNJhTSimllFJKqVpIgzmllFJKKaWUqoWOeTBnjJlkjNljjNlr\njHngWO9PKaWUUkoppf4OjmkwZ4wJBP4HnAn0BS4zxvQ9lvtUSimllFJKqb+DYz0yNwLYa63db60t\nAT4Dph7jfSqllFJKKaXUX96xDubaAwd8Xsc573kYY240xmwwxmxITU09xodT+5SUuZizLpbwxJzj\nfShKKaWUUkqpP5Hj/gMo1tp3rbXDrLXDQkNDj/fh/Oms2pfGg19t518fbTzeh6LUX96G6Awe/Gob\nRaXlx/tQlPrbyswv4b65W9kRn328D0X9SexLzeO2OZt58KvtFJdp/ayUr2MdzMUDHX1ed3DeO6aK\nSsvJLy77w7c1e3U0k19bTmHJ0atoUnKLAYjNKCAhq/CobfdYysgvOd6H8JdVUuZi6v9WcsFbq7DW\nApBTVEpuUekh180pKmXSq8uYtSr6GB/loWUXlLI9LpuRzy7m6R92HXTZ4rJypkxfwchnF7N2f/ox\nPa4nvt/FnHUH/vSdyIz8Es/1V4fPWsvlM9bw7E/hx/tQVBXWR2fwxYY4zp6+guScouN9OH+4rIIS\nMo9TO1pa7iIl98jPeUFJ2TE59m82xzN/awJz1sWyJyn3qG//eLLWkpRdhMv116jTU3KLKC13He/D\n+Fupc4y3vx7oYYzpggRxlwKXH84GSktLiYuLo6io5pVLSm4xJWUu2oTUo07A74tXU3KKKLfQNiT4\nkMt2oJC7hjdkx65dNKpXs1MbHBxMhw4dCAoKqvLz9VEZnr+3x2fTrml9UnKLWLM/g7G9QmkcXPV6\nx8uiXclcP3sDL198AucP6XC8D+eIrNqXRsdmDejYvAEA2YWlLItI5dQeLWnaoO5xPbYNMRlsPZAF\nwMdrY7l8RCeGPbkIi2XPk2cSEGCqXTcyOZfdSbk89t1OLhnekeCgQFbtTaNzy4a0b1r/mB73isg0\nmjYIon/7EPal5jH+paWez37YlsjDZ1X/u0iJWUVsd4KrbXHZnNi1xTE7TnciIrfo6CSDjoWtB7KY\n+r+VPDS5NzeO7nbI5VdEppFZUMKEPq2pXzfwDzjCP7/8knJW7Utn1b50Tu/bmqGdmx/vQzruXC7L\nwl3JFJaW0b9dCD1aNz5ux5Lnk0DdEZ9N6yaHbn+PlLWWReEp5BV7E2KndG9Jq8ayz40xmexLzaNj\nswac3O3o1z1FpeUsCk+mcXAQY3qGkl1QyqAnfgFg3cPjadU4mKLScpZFpDK6ZyjBQcf2Hr7lk038\nsiuZeTePZGjnZoe9/lmvryAqLZ/vbxtF//YhR+WYErIKmbPO+8ROZoF/8nJpRCoZ+cWc2KUF7Y5x\nW3YsvLQwgjeW7OXm07px/6Tex/twfpe1+9O55N01tAsJ5pe7x9Cwir5wYUk5v+5O4cSuzWnZqN5x\nOMqja1NsJsnZRUzo25qgwOMz4fGYBnPW2jJjzK3AAiAQ+MBau/NwthEXF0fjxo0JCwvDmOo7qj77\npNTp+DWpH0TnFg0PuY7LWpJziggwhlaN6/ntpzROOs6924ccdP/p+cWUNpaRs8AAQ592h67ErLWk\np6cTFxdHly5dqlxm1T7vSMQP2xI5o18bXvklkjnrYrlnYk9uG9/D/zjyinln2X6uOqmzJxg52uIy\nC/hoTQy3jOlOSAP/YPL9FVEA3Dd3G3uScrlrYs/f3fhsis3kq01xnDuoPcPCvJ2u3/aksCcpl3+N\nOXiHduHOJOIyC/nnqC7EZxUyY9l+pg5qx+BO0lDtTsrh2y0J3DG+B9mFpVw+Yy0DO4Tw3a2jAPhg\nRRSvLY7ktnHduXhYR2avjubm07rTvOEfG9j9uD2RWz7Z5HmdmltMfkkZJU4GLC2/2NMBqcqCncme\nv+dtiqNDswZc88E6RnZrwac3nMS+1Dy+WH+AW8d1r1GSYM3+dFbtTeOOCT0JPEgQmZJbxJXvrwUg\netpZzK4wMnio+zrdJ8ubX3Lsgqz5WxOIy5R7OKcGI53HS0SyZKWf+XE3HZs14MwBbatdNjnHe+6f\nOW8Al5/Y6Zgf396UPGatisZlLWEtGnLD6K7HfJ81Ya3lraX76BbaiK82xXnev+Ct1ex5ahL16hzd\nTnJBSRmvLY7kvMHt6d2myRFv54dtiWQVlnDFiZ0Pa72I5Fy+2hTP7eO706DuoZv6N5bs5eVfIgDo\n1boxC+4afUTHe7iW7ElhZWQad07s6UmC+iZTftyexPg+rY/Z/rfFZXPD7A1+7102oiP3T+rN9F/3\neto0gE2PTPSr999bvp9urRoxtlerI97//K0J/GfuNgB+u/c0inymEEYm5/He8igKSsr4eE0sz54/\ngEuHd+SNX/fSolG9g97PX2w4QJ0Ac1hJ1Zkro/hll7QTcZkFWGv5Zks85w/pwBCnvYxKy2fmyijO\nG9KBQR2b+q2/Iz6bqLR8AGatiuaFi06o0X6ttbz52z6a1A/iqpMql/NnfgwnLa+YCX1asSg8hdmr\nohnTUx7L2ZeaxzUfrAPgnBPa8fplg2v8fY9EdFo+M1dFc/mJnejpJDwqHn9+cRnTf91LUWk54/u0\n4tQecqyJ2YV8sCKKG07tSqsmwZS7LC8u3MNbv+0D4K3f9nH9qC60aFSPcpfllV8iGNs79LCSTQcy\nCnh/RRQXDu1w1ILpwxGRkgdAQnYR5/5vJT/ecWqlAGf+1gTum7eN8we3p01IMH3bNeHsge0Out3v\ntiYQnpjD3RN7/iEBU0mZi1cXRTB5QFs6NKvPW7/t46qTO9OhmX+/2lrL+W+uAqBbaENevWQwAzpU\nfd5j0wv4aE00N43pRoujHMQe65E5rLU/Aj8e6fpp2XnQKJSK+TCXzxSjAKczaK31mxJZVn7wIWtr\nLS4rmbFUZzpjswZB1K0TKNv3Wb3cZQkwgJH9WWuJzSiguMxF4+A6nvXdy+YVldEo2Ht6swtL/aaL\nNAkOok1IMC1atCA1NZXP18fy/bZE3rtmmF+nIreolPMGt+frzfFEpuRRWu7ybOelXyLYHp/N21cO\nZe7GOL7bmsAp3Vvy7rL9vLtsP73b+GdW6wUFMu38AXQNbUhUWj73zd3GRcM6+lWe+cVlBAcFHrRz\n/t7yKGauiqZX68aehsJaS0FJObEZBXLuXZZ3lu0nLa+Ely6uWYXua866WGatiuaU7i1JzC7kx+1J\npOWWMCysOdZabv10Mz9sTwSgWcO6XDikQ5WjUksjUrnRed7wshGduH7WBsITc4jLLOS9a4YB8Og3\nO1kXncGpPVry3ZYEQBr4sAd+8BvNSMwuYu7GOGYsj2JddCZf/utk6taRSqWkzIXFVuoQlpS5MEbK\n6+F0FkvKXAQFGspdlhtmb2BC39Y8//MeAOrWCSAowFBQXEZBsbfh/25LAlMHteeWTzZy4+hunNqj\nJcFBgZSUuUjIKuTdZfs9y05fvJexvaWBSXLK08yV0Xy0JoZfdiXz852jPd+t4nHVrRNAfnEZl767\nBoC3l+5nzo0nVZvFTcv1BmMul/WUEbf4rELOnr6cO8b3ZGLf1jzyzQ4a1A3kwcl9AHjye+80zIpT\nnq213PLJJnq0bszdE3sCcs1fWLCbW8f2YEKfVgQY4ykbZeUu8ovLuWH2Bq46uTMT+7YmOCiQ0nIX\nt83Z7Nnut865BMkK3z5nM3dP7MnwLs09DcltczbTrEEQW+OyOaVbC+5zMqrlzlSZwADDlgNZ/Hf+\nTp6c2r/KhrWgpIw6AQFVnuvqfL7em6F++JsdTOjbmjoBhuIyl1/ipLTcxQGfcx2Vlue5T+vVCaBO\nDRvEjTGZPP7dTv49thsT+rSmuMxVZbbV7YOVUcxZF0uDoEDyS8q5eHhHGterQ5nLEhRoapSUO5SS\nMhcr96bxvyV7efOKIbRyRm7KXZZC53nHAxkFPPDVdi4e1oErTuzMlxvjPPdQRT9tT+Lcwe0pKXNR\nUu6iYd1Az3HGO9f/nok9Gdm9pWf/Fa/Zsz+FszwijYfP6sMp3VuyPjqTd5bu552l+xnQPoRXLhlE\nUnYRryyK4JWLB9GphXQK8ovLuH7WBs4b0p6Lh3X0bP+bzfHM2xTHWmd2xtr9GXQLbcQdE/wTeBXt\nS83j0nfXeNqkk7o2Z1T3lpWud8Xv8P02qfsuG9GJOeti2Z2UQ4dmDQiuoqxsis3k6R/CeeHCgXQN\nbXTQ46mOe/8PzNtGck4xw8KaM6FPK278aKNn9kFggGHepjj+c0Yv2lSYHbM5NpNHvt1Br9ZNSMkt\nIrOghKfOHVApwAC5z4ICA6rsBO5Pk87nh/8YTpcWDblu1nrmrDvgNxLkdt6bK1l09xiCAgNIzyvm\nqR9kmu7/ndWHp34Ip2toQ965cig9Wjcmv1j2GWCo9twXlZZ7gh+AmauimeATuM7dGMfXm71PpuQU\nlhKVls9LTtD95cYDfHDNcOoFBfgF7EWl5dznBIi92zShb7tDJxMW7Ezi8fneujavuIz3lkfx884k\nkrKLmH7ZEOrXDeSrTXHMWh1DRkEpT5zTj5s+3kh2YSkN6gZygs+5j6lQz1dUVFruqa+i0wt4YYHc\nm7Hp+Z6ZGu8s3cePO5JIySmifdP6vH7ZYPo+uoAVe9M829kYkwlA43p1yCr0JuGe+TGcbXFZvH/N\n8IPWVwA/70hk5qpoZlw9zJPItNZinL6eb9367ZYEZq6KprTcxePn9CMoMID/zt/FTCdJefmITvR7\nbIFn2zNXRdOnbRNuGtOVxOwiZjj9p62PnU5cZqEnkBvQPoTt8dks3p3CxcM6sjcljzeW7OWNJXv5\n+c5TWR+VwSdrYwkwhvvP7M3Ibi0ICgygtNxFuct6ju+bzfHMXBXNzFXRnj7gFSd1rhQkW2tZHpnG\ny79E8OolgwhrWXngIzI5l/vnbePuib04pXsL3lq6j++3JnLdqC58vDaGMT1DuXF0V9bsT+eFBRFc\nOLSDp71uGxJMZEoeuxJy/MoFQEaB9Al+i0j1zIb5eE0M5w/uwMXDO1LRj9sTud1pn2eviqZj8wak\n5hbTpWVD3r16GM0b1sVa67QxAZ7vV7FNBHj46+1sjMnkpK4tePycfn6fPTBvG/FZhbx26WD2pebx\n5m/7eNO5PiDty71n9PLbZlGpdzrpvtR8pryxgsinz/Sra1Jyi7jpo41sipV6bcbyKLq0bMiEPq0O\nOivpcBzzYO73yioopV5xmacjAHKR9iTleubkdmregKYN6pKUU+RpwIKDAj2dqtJyF2XlLuo7lV1B\nSRl1AwOISsv3NPxuZS5LoMvF7qRcz/oAu3x+TbJT8wa4rCXbqTiq+rGE2IwC+rZrQklZOUVlLtLz\niiktc9EouA45RWWk5BYRFGho0age1lrun7cdgPVRmYzq0ZKcolI2xmSSU1RGp+YNuOLETnyyNpYR\nTy+ipMxbeBbuSiYhu5D75knF7a7kTu/bGt8+U1m5ZfHuFM58bTl1AwPo0boROxNy2BaXzRn9WhOd\nVsDqfem8siiC/u2b8P1tp1Z7Tdwdat+pMNN+2s07PsGC27xNcYzs1oILhh7elMuvN8ezO0mmBdZx\nOuLp+d7nB92BHMgo4JtL9rL4ntMIDDAcyCigzGXp0rIhS3aneJb7bmu851dBF4Unk5lfQpP6QayL\nls7S5TPWVjqOReHe0aytB7I8meOtB7IY/vQiVj84DpeFkc8uJqeojCen9iOsZUOGhzUnIjmXc95Y\nCUBQoOG5CwYyeUBbT0WQmlvMjgT/Z7PqBgZQv24g57+5igl9WnPNyM4s2ZPKkj3eX3p97ZJBPPrd\nTvJLyv1Gqp76IZzYjALWR2eyPnoDAQY+/McIrpu5nsZOYuHFi07gh20JLNmTyryN0klo4ASr7mPZ\nn5ZPz//7ifAnJvlNy/thWyL//nQT15zcmfN8sr0l5S6emL+Tx8/p59eYDunUjJD6QZ77BOCz9QdY\nsieVgR1C6Nm6Mam5xSyNSGVHfA6fr4+lbUgwH62JAeDByX1YuTeNLQeyaNMkmPySMvKd51GLSsvZ\nEJ3Jx2ti+HlnEj/tSOK0XqFEJOXywFdyL729dB/TfgonrGVDZv5jBBtjMrl8xhqKnfvHfd2rkuk0\nNvnFZby+OJINMZlc/p6Uj0V3jyE4KID5WxP8ysbwLs0JbVSPu7/YQlZBKc9fOJBrP1wPSIDzyFl9\naeaT1Z+7MY57v9xK0wZBTL9sMGEtGtZoNN131CIjv4S+j/5MabnFGPj8xpMZ0aU5yyNTuer9dZ5r\nC9KAzFguowxdWzZk8T1jahRYLY1IZXt8Nq8v3sv0X/eyMyGHB87szU0VRsQTswtZH53Jp2tj6d++\nCVec2JkHv9rO8KcXEWCk0RvZrQXPnDegyo5DTW2MyeCCt1Z7Xu9MyCE2o4CSchfP/BjOjnj/X/7d\neiCLdk3r881m/8e1GwfXoWtoI7YeyGJHfDZn9GvDydMWk1VQyindW/D4lH6UuSxfb45nY0wmz/60\nm7tP70leURm3zdnM/ZN6c/Np3Tz7mL0qhsLScq54by0rHxjHgp1JAHRu0YDt8dlMeNk7tXh7fLYn\nmNuXmsfq/ems3p9OUnYRkwe0ZeIrS6n4SOR3Tnm7Y0IPNsdmUlBSzgif5IKcm0wueGuV33rXfrie\ntiHBLLn3NLbHZzOsczO+25rAnZ9v8ZSXyORcIpLzuHZkGJP6t2HOulgmvbocgJD6Qax9aLxfB+a/\n3+1ka1w2H6+J5dEph98ZuffLrXy3NYHFd48hOafY+X7xtAkJ5lefOnva+QP4z9xtnPTsYp45bwA9\nWzdiaOdmGGN4dVEkO+Jz/K73zJVRTB3cnibBdTyjGZ+vj+X+edtpGxLMivvH+SUqY9LzuevzrQAM\n6diMkAZBtGhUj32p3gAL4M0rhvDQ19uJSS8gKbuIjs0bcPPH3lkS7qBuf2o+X2w4QFRagaft6NBM\nghD3yNZHa2J45JsdXDCkA/OcEeLmDeuSkV/CovBkv7bNHci5R6R+3pnEt1u89c7m2CxGv7CE3KIy\nnj1/AO2a1icxq9BTBwK8t2I/Uwe1JyjQMKxz82oTR6udWUAr7h/LqOeWkFdU5mlzF4Wn0Pexn/ng\n2uGk5UndOH9rgqcObBsS7Gmv6wYGcFqvUBbuSiY9r5jgoEA2xWYypFMzGtarQ0pOEffP28aSPalM\nvxdI38QAACAASURBVGww8VmFTPtpt+c4ftqRxMNn9WXBziSe9Xl/XO9WNKhbhwfP7M2zP+0mM7+E\nuMxC7pu7jXp1AujbrgmRyblsjs2kRcN6nuTlnuRcz7mvzhPzd5GQXcS+1HwGdWzqeVzkh9tH8dHq\nGD5bf4B7JvZkTK9Q1jjPbX+yNpYFO5NZ/eA4lkV62+eqnkkPT8zhjs+2eF6Xllue/H6XJxn+0XUj\nGNypGf0fW+B53tB32u/UN1Z62q3AAOMZiXzt0kHc8dkWggINP91xKt1bNWa9E9yCtO0x6QX8sC3B\nE8y5XJZ9qXlM/3Wvp0654r21PH1ef4aFNff0cbILS3l1USSbYrO48v21XDeqC6v2pROemMM9X8o9\nszk2i1cXRXr2N3OVtC8DO4Tw33P6cd6bqzxlyFee04b5/r7Cmv0ZrNmfQacWDRjauRnrojJo37Q+\nYS0b+vXD8kvK2e08M5meX8I3m+OZ1L8NLy2MYPHuZNY9NIG6dQJ47LudzF4dw61juzO8S3PCWjSg\nsLScuRvjKC5zEZWWz5ieoQQFBjCiS3Nyikr5zEmUDnnyl0rHDPDeiijeWxHF21cOpUOz+gQHBdDE\nCf5bN6nnqcuWRaQyvk9rcorktwG2xmV5Ajm3qLR8vtoUz61jexCTkU+zBnWJSstnRJfmRzSb7U8b\nzCVkFfLNlnh6OH0f35E4l7V+D1fGZhSQVVBKTlEpdQMDaN+sPtmFpWTkl+ByWXYn5WKtpWMzCcLi\nD/JDIvnF5QQY4xfIBRpDuc/+fYO3+kGBfgFhnYAAGtYLJLuwlPS8Yr99hTjTPkvLXYQn5pCaW0yL\nRvX85n/fMHsDK+4fy+uLI5m1Wjq1HZs3IKS+FBj3smN7hRIYEMCi8GRGPbfE7zs8f8HAStkNay0D\n/7uQ3CKZlrczwdsA3jh7I1sOeAvajvgcvt4cx3mDqw7A3COhH6+J4eqTwwDYGpdVablPbziRy2es\n5Z4vtxKVls+oHi2pVyeAxeEpBAcFcPXIML5Yf4AxPUOJyywkv0RGmjq1aMA6n2cFy5xrsT46k7S8\nYr7YUDljGp1ewLSfwnn4rL6c+dpySspcRDx9Jml53orEHTCP692KX3en8M2WeDpV0Xl+5rwBlLlc\nlJVbnvAZFYpMySMyJY+Q+kF0b9WIjTGZJGYXUe6y5DiV0yPfyiziwZ2aEug7XbfccvcXW/lyQxxz\nbjwJgP/M3cpve6r/5zgWhSf7VWIAj03py5kD2vLcz7vJLy7z/NjOhD6tWRSezGynzAC4rGRby1zW\nU27OHdROMvXPLfFMz0zKLmbaT7vZXKGyuW/eNp6c2o+mDepSVu7itjnSeZm1Osbzfa86qTMfrYlh\na1w2573p34k8a2Bb+rVrQjOf5wwf+lquwZSB7bhhdFdmrYpmaUSq831TWBSe4reNXU45/fKmk7n8\nvTV8ujaWW07rxvytiTz3826/Zc/32X9QoPGU6ej0Am6bs9kv+KrO6gfH8dLCCOZujCMhq5BP18Z6\nKni3iORcnq+wb4B/fLiewABv3eEO5AC+2hRPuctySreW1AmUqU+RznTJrIJSrnp/HU0bBPGPkV0Y\n36dVpVG8H7cnsishh7MGtiWnqJSLhnagbdP6vL44klJnBoK1MiV4RJfmnmcMC0rKCQ4KYPY/T+SB\nedvY74wC7E/L56aPN3Lj6K5VTuH5ZnM8e1PyaB0S7Bmx8U1oTftpN+N7t/J7ruqfMzd4kiV3jO/p\nqaN9k0+r9qVz5ftrWXH/OECms360OoYLhnRgeWQqgdVMC8sqKGH26hgSs4tYFuF/z6zZn+6XSJrQ\npzUjujTjmR+91+gfPtfCbdl/xtKsYV3GvvgbyyPT6NmmMVnOfbJybzoTX1lGnQDjqX+2x2f7bcd9\nD545oA1T/7fSb9unTPvV8/d3t47i4zUxnpEHwK/N8O3QvPxLBP9bshdr5f75YZu3Y+/2vyV7Pdt6\n6aITPImy9LxiTyDXr10Trjk5zJPkS8wu4pVfInhn2X5GdGnuqV8jknPZm5JHfJaMoozpFcqIMP/y\nkF1Yypcb4zydwf2peWyNk/L1045ELh3RkflbE7AWerRu5BnRrk6SM8MB5EfD3H7cnsTuRO8PW0we\n0IazB7bjvnnbsNZbd3x6/Ym0ahLM0ohUGtWr45dU/GZLAt84wc7Pd55K7zZNeHvpfs85yCkspVnD\nupSUuXh/RRRvL5Ws+50TengeGfCtt684sRN92jZhQh8Z/b7xIxmF6ohMa/f1r9FdeWfZfk/CxC0u\ns5Dz31zFuN6t6NCsvqeOnucz1XdEWHMCAuQcAAQHBXgy/oM7NeW9a4YT9sAPfnW0u+51J3ce9Ang\nAG45rRtv/vb/7N13eBTV+sDx7+ym90qAJKRAQiAktIAUQaoUKQIioNJRERQsPy4iioooolwrcr0C\nigURlCKCdIh0QgsltAQCKYSSBult5/fHZoddEpqAmOv7eR6eh92dnTnZ3Tlz3veUOcXS/aks3W8M\nCp94oBZBno6E1XBm92nLZNb2hHTqVHPS5k9PX30cT0cbwqo782hjX95ffZxVh9K0785kRr8I+jf1\nJ/i138kvLsPLyYYHgj1Zd/QCyVkFrIs7z+zoU7zQoQ6vPFyXlxcf1JLOJ87nkJx1tQevpqsdV8qT\nf+a/BUBLSJqGuX219bTWq9U0wB0HGyvSLhdWuA59v/OsRTC3+fhFrTcv0s+Vh8Ora9czU+Jx8nLj\nZ7n7dKb2mf97/UmtR9QkPbeIjNxiMvOKtcSleZvB5Ok2QRaJtEs5RSyMSdamerjYWeNoo8dKp/Dd\nzrM80zbYImlnCuQ2vfIQXT7Zgqn2MAWIJWUqCRfzqO3tpNWPnw1qTK+GNRn7435WHUrjjeVH8HGx\nZWFMcoU2cGp2AcO+2cMzbYNp4OvKyfM5zNqcYLHNyQs5ZFYSmJm3gZMzjfsd1yEET0fjMMKFMcl4\nOdkS6Xe1dy73BosKnjifwxebE9gab/yNvP5IPdJzi4n0c+VQeb1TzdlWWxxw6sqjFp95Zl4x1V3t\n2HvG+B3P2pwAlk1kwmu6EHfuCsPnG+vz6X0juHil4t92PaN/MI720imw5kXjcPTXutcjvKYrnT76\ngym/xtGxng8zVh9nwe4ki/e+2bM+jrZWbE9I57eD53jl51iLdk+wlyPdI2rQ4jbXBvhbBXPmicjZ\n0Qn8sCuJOb2M80FOXcwjyMsRO2sdZzMsu+/1OkWb46LTKTjbWWs/FvOeD/NKwyS8pqu2zG3CxVzS\nLhegU4yVmZ+7Pc621thY63mkz+P8Z+43ZOUXU1JSSqOwYCIaNeXHX5bx04Lv+fjdKVSrXgMrvY7I\niAhenTFLO2GqOdviYmeNbXm0ba03RvNXCks4eSGH/OIydAr0beLHL/tSGLNgP3bWekKqOfHxgEbU\nq+GCqhqHD5ku4k+1CKB+TRetse9sZ8WiZ1piZ62rdNiLoihsePkhikoMPP7fnVhbKbzWrR7PLdhv\nEciZvLToII9E1GTqyjhKy1Sm943Qsvi/l2cOT17I5YH3NmBjpdNOYhsrHTP7N6R+DRfqVHOiWaA7\ne85kacMFzK08lMbx8zks2pNMfPk4a3OmiyPAuA51+GxTAssPpGrD9la+8CC+bvakZBXQc9Y25mxN\n5GDKZe27X3MkjZWH0ogKcOe9vhHkFZViY6XDz92Bhm+vY/fpTK5dPCrA04H+UX5attvV3pq3f4tj\nWOsgPttozEAFejrwYqcQBs+LISO3mNLyRuuMfhGE+jgz9OsYi4vudyOaM6Q8k7bzdAaqagyuok9c\nolM9H8a2N2b3ywwqj325kxt5qrxBZW9jxYqD57ThC30a+2q/hQhfV6b0rE//L3fyo1lFYlM+XKqm\nq+UE8fTcIr784xS2Vjo+HtBIm5f328FzNAt0Z0jLQHIKSzGo8ECQB7sTM7WM8ag2QbzUOZTh38Rw\n7HwOM/pFEOjpyKSlh1l1KK3SxqiDjZ5HG/tqf0+r2p68s+pYhUZ6/y93sOdMFrZWOvzc7Wno50Zy\nZgHf7zxbaUBv0tDPlafbBvP8j1eHTZoCuTYhXuw+nakFsuYeCPKghqs9zQM9+GVfCk/N2014JXNf\n18Wd50xGPoGeDsx6ogm1vZ1IuJjLHycvMnOd5cW+mrMtPz3TgteWHebX2HNaVv3VJYe1Mpiy8tn5\nJcYheBtO0ibEi9e616NeDRcOJmdr38mZjDyuFJTgYm9NveoVF6jYn2S8gJn3hj7TJpjmQR7U8nTg\ndHoedaoZy7s27gJr4y7wxAO1qF/Dhc3HL/J6j/q8sfyIxTCm65m++jhfD2vG/O3GoVimQC6sujOd\n6lXTMv0m7/QOZ23cBbafSteGML2y+CDrj17gckGJlkl/OLx6hQWkfjuUps3nulaCWd3hYKNnTPva\nNKllGcy982gDGtR0Yd62RFaW/yZdyhNkLYI9WBiTrA1LM8+wlhpUXu5sHP5bWFLGf/84zZryHjcw\nNhR+3nf1tzioub/F8Dxj3W/F2PZ1eLi+D2mXCxnydQw/xSSxIyEdL2dbbfSAp6MNGXnFFJUa8HC0\n4YsnmjCxSz7WVgrjf4rVAjDzoPDjDSe14+8ya5x/PawZ3k62zNl6WqtbTXWpeaIs4WKuNjwMoI63\nEzqdQus6nuw9k8XaF9vSbmY0mblXA860y8Zh2TZ6HVcKSvh0YzyrDqWhKKAAXcKr3zCz/OrSQ9r/\nTQ1cUx152mzIYa+GNbG30bNlQnvafHC1NfbE3N0ElvdqzugXSWK68W9Y/GxLLheUEH8xl3/9coi0\nbOPQPPNhjBl5xbg72rDjVLqWDNLrFMa0q6Nt07qOJ3vOZPJWr3AGNa+l9eSZFr8y9dpfKShhYDN/\n9pzJpLR8+NW3O89oQdiYdrUpLjUwt3zOnXmPY1h1Z6b3jeBgcjb/Xn+S4a0DyS8p04K59/tG8uIi\nY0O9XahxPl7HsGrsPZtFaZmB4a2DGNwyQBvFYFLT1Y7Q6s4kXMxlXMcQiyFigMX1wPS3mxvYzN+i\ntz4rv5jRD9VmVJsgPlx7QgvkejWsqfXqDGhmOW/Pxc6aJrWM16XMvCKtvXYuu5ADSVlsS0inoZ8r\nR9OuVGgTtA31ZtHeZAwGlYy8IlzKRzKZ9gvQrUF1AC2QA3j2odosuSbINFl2IBVPRxtaBHvyy74U\ndidmWCTQHWz05JcnRS8XlDBp6WHt/N94/AK5RaW0qu1psX4BGBMAn2yI56l5u8nOL+GRiBpsOXmJ\nnEoClcea+qPX6Zi37TSvda/H6fRc3vv9OG+tMCZ/Xe2tURQFTycbUrMLOJORr7Vjarrace5yIf/q\nWpdgbycea+rPr7Gp/Lt/Q6q72pFdUMLwb/aQlV+sfVZj2tWmV0PjHLTmgR6sOpRW4bdSmYW7kyot\nf7u63lri2dRLDMZeXNO0G3Pujjb4uNri527P+qMXKCwp4/uRDwDGQM60vV6nEODhYHHe7z2bpQVy\ncLXXu11db97qWZ9PN8YzuEVAhcDa5HJBCdVd7cjMK+bBOl688nAoYxbs1+otgJEPBhHq40xJmYHB\n82KYtSlBa6/7e9hr7dlhrQIZ2ioQK51iUQeZGFR4t7x8LuVJflMSLuFiTqUdRx6ONvRu5EteUSm/\nxp6rkMA+m5nPrM0JFj30t+JvFcwdSTU2xJ1srSwu0AClBgMJF3MJ8XGyiOoDPR1xsbcmr6iUU5dy\ntSF57g42FvPY/NwdSLkmmAv0dESvU7Sx5qZtTF+Ag40V1lY6HB0dSTl9Ai97hZxCHavWrMXbpzoG\nVGq62eNkZ0Wffo8x76svtX0fS7tCSZnxolzdteLqSn7u9iRnoS0pP7O/cfXHwymXtTkSXcJ9zDL0\nCg+FemsX8treTtRwtWf52NZ8suEk7/RucNMhWqYVwXa91hG4upCCubDqzloXdujrq7Xne0TW5HJB\nCS8vjtWyRIBW6YGxy//arOynAxszedlhAjwdtRPYFKSZjlNZIAcwsHktrQHyUudQvtp6mmmrjqEo\n0NDfTfts3B1t+H1cG979/ajWSwEwunwYTP8oP22iskmbEC8Op16u0KP4x4T2Fo/7NfWjX1M/LueX\naMHcm73CsS9vrAyas0vriWka4E6das4sHt1SG6I0+8kmPFjHi75NfLXsaOv3N3GpvMewY71qWnbO\n3JQe9RnxYBAbjl7g+YX7qVfDhbfLx+eDMbN0LO2KNj69VW1PfN3sSc0uoHUdL6Iqmb/2dBvjIjvm\ncwvnDY1i5LfGyf9H3u6CtV7H0aldePGnWNYdvcCbK+J4Z+VRGpZn1R6P8ifEx4kfdiWhU8DXzR4r\nvY5fyxeLMQn0dNS+X4DhrQP5ZvsZAI5O7ao9r9cphPg482zb4ArB3J7yzJqjrRWKojDriSYkXNxS\n6XBeczMei8TXzZ7O9X2I9HVld2KmFpxM7BpGA19Xnpy7i+0JVy/Oq8e3oV4N47ySx5v5syX+EisP\npXH6Uh4tgj34ZEBjnv3BOJfHlPn/fuQD2jkX4edqEUABTHu0gRZ8j3ww2KKxbR5M7n+jMx+vP8mn\nG68OV9kan063T7dirVe037SXk60WiLjaW9MtogbDWgWSnV/Mvx9vxFdbTjNjzXFCJv+u9SY9+1Aw\nLz9cF4ARrYOw0un4d/+GLNyTpA1tMm/gbSxvcDYP9GBanwZ8sOY4RaUG3uhRnw/WnKCotIwWwZ58\nuPYECRdzOXkhh+92neV0+bC0lzuHMq58UaZwX1c61fNhSMsA2pYvVlBUamBbQjpBkyynUZtfvBuU\nzzdpHujBM22DeWHhgQrD4QEa+bsRm5ytlXn9S20rXYHx4fo+9G3si6OtFb5uxsZySDUnrSE7vW8k\nbg42WuNwQJQ/n2262shsHuSh/TbCa7qwJu48T7WoRX5xGUv3p1rUgWHVXXi0UU2Wx57jqRa1mPZo\nhPZaiI8zNcp7PfaezWJvee9ALQ8HekTW4OMBjRj2TQzbEzIwnaKmoZiLn22pfTa5RaX0beKLr5s9\nuxONCSnzuZFH3u6iBcPrX36IlYfOaYmN/k39iAp0Z1tCBuvizldohJl6pxaMamHx/McbTjJrczzW\nep02N7ZbRHV+jT3HqkNpdAirRr8mfoz9cT9hb6zRpkSYM6+bvZ1tKSkzkJ1fQpCXI21DvbUkg4lp\ngQB/DwfcHKy1XlMw9rabPrtHImvwfIer8whNPQLD5+/RphoMaxVonI/20R/aMD0w9np98UQTi6GH\nz3cIsdifiWnhk8HzYqjt7Uh6bjFuDjZsfKWdts3TbYL5fFMCU3uHM6RlIClZ+Ww8ftEioGxX15uZ\n/Rvi5WRL41ruDGttrJfPZlzdpnejmjT0d2Pqb3E8HG6cQzdvWDOL8hgMKn0b+/JAsAff7TxL3Lkr\n1PJ0YP7w5to24zuGcPJCDquPnLd4b8tgT155ONRiQTFzj0f5sXhvCq91r8eoNsYFjGz0OgoMZYzr\nGMLLnUMJ8HTQRumY6x/lr61QOOrbvVrCdMn+FK03clL3eoxbeEDrXWkT4sX3Ix/g622JqKqxAf/d\nzrMEeTnyeJQ/R84Zh0GD8fplmtcJcHRqFxxsrPg11nIY9aJnWlDNxY72M6OZuy2RpQdStV7wse1r\nY6PX8/GGk1ogB2jzsky/RdM14pHIGly4UqgNv53Soz4N/V35ZEM8CRdzqevjzLMPBfPFk00A48JT\nD7y3EUCbrvBqtzBe7WZaqdIHP3cHvt1xBi9nW3zdjfXCV4Oj6P3Fdjp99Id265klY1pRw6wNOb1v\nBNP7Xq1XTCPFJi09rPXOms+RHNoqkMsFJddNhvVqWJPMvGK8nW1JzS7A1kpHi2BPjqRe1obDm98W\n67l2dfB0tMVKr+Dn7sBbvcJ5q1c4b/8Wxzfbz+Bka0VYdWdsrfRsm9iBlxfFsvRAKu+uOoqznbVW\njicfqMW7fSKYvz2Rt347SpdwH3adztQSrz+MfABbax39yxPcgZ6ODGsdpJ0vz3eow6tLDhObnM0J\ns7Zsl0+2aCNk+kf50biWO/7uDhbBnJ+7g9Z+fLpNMHO3GtsUtb0d2fhKO95YfoTvd52lWaAHQeWf\ngakHsn9TP37el4KNXkdxmUEbWRRZvr/hrQJZdSiNL/84bTHyqk2IlzakE6iQKH62bbC2TsBH609q\n7c1b9bcK5gDOXy6gppu91vCxNatkVVSLAKS2t5M2sdXBRk8NV3utK/7aic5u9tak5+othkheO3bc\nw9GG/KJSMvOLcbS1sjh29+7dWbVqFREPPsyq5b/QtXc/Du4xLgDh7mCjzcczsdWp9O/agY/+/SF+\nnToyadIkdDod7777LmCcEB3k5UhxqYHCS1a0rG+sqJ59KJiXFx8k0NOBF665oNSr4cKkbmHYWOkI\nKL/IN/J3s6i8b4f5krAz+zfk9KVcujaoTm1vJz7bGG/RaDatiGfSrUH1CheIyobX1HSz55vhzSkp\nM2gNh6fNetzMu8udba0sskKeTjZ8+VRTrHTGRRNquBqzrJF+bkzqZrl8b/2aLloD5HJBCQ3fXgfA\nh49F0j+q4oTamq72WgPS1OVuarBVxnzVThc7a4K9HHmtexirDqVxMOUyAZ4O1C7vETVf5r+WhwM6\nncJHjzeiWaAHk5Ye5pxZZrt3I8sVnEwBWffyFQo71ffh+DvdKpRnau9w9idlcfpSHq1qe+LuaMOC\nUQ+w9EAq/Zv6oSgKnw1qTGZuEYdTr7BkfwoBHlfnKZmGJ3Ws58M3w5qRUz5ZH4xJjK+GRLH+6AUO\nJGXx9fZEreFp6s0AmPxI/esuovFCxzrUre6Mn7s9NlY6ejfy5cE6Xte990zzIA+LXo0XOxmzysWl\nBovPqEdkDYsgESr+bmq62eNsZ82cIcYFbl4AAl9dBaANVzYF4P2a+FG/pkuFxYJm9IskpJozRaXG\n1ciqu9qx9LlW1H7tahBSzcVyNSrzBRqaBrjTs+HVcneu70Owl6NFBhKMQQUYG7dgXEXQdGEa0642\nP+9L0ZJSnetXY2FMMrZWOh4rH1pnPoH7saZ+FJSUaT3FUYHudAi7uphC21BvLaga/VBtzmUXWAzL\nNTdvmHEhgLlDrzYgTQsGgXHI5apDaTz88RbA2Lv1QJAn/aOuDpF0tbe2eI/532nSJdyHtXEXtF49\nczFnMm84r3H52NYWQbn5glMA84c3I6+ojEcir672+cQDtbC11vN4lOVQzkciamjBXId6PoxpX4e5\nW0+j0ykWC/v0j/Kn1KDyaGNfAj0dtARNI3832tX1pkdkDYa2CuSTgZWvqGdfSY/VpG5h2oqk0x6N\noP3M6EoTPGAcFrbjVAYDm9XSGgVwdejl8NaBFXo1TSvcejraMLV3A+xt9AxoVotXlxyyGEJsb63H\n6QarXg5uEcjX2xO1erOu2TnTyN+NDmFXV3R8KNTbIoGWlV+iNb7HdwwxJiEKSlh2IFX7Lmb0i6Tf\nf3bg62bP4JYBFguZzH6yCeeyC3kgyIOn5u3Wenuc7SqW18v56rBuVTW2IV5+OBQHGz2zo09pgdzQ\nlgG83bvBdf/ea9X2vlp/mhr1ntesaDy0VSB21nqtV8TP3YFV4x6k/pS11Kvhwurx15+LXsvDgbd6\n1sfHxQ5FUQjycuSbG1zbdTqFjwY00o6zPSGdjvUsV9V8qXxRqA1HL1BcZuBSThEN/d0qXSTGXJCX\nsV4yDyJmPWFcFGLkg8bg7pXyJNG1nmtXG1VVebNnfa3uWrA7ySLZ1SLYk5n9G7I7MQOdomiLvvRs\nWJOpK4/yw25jvfRYUz/Gtq9T4Rjv9WlAqI8TTWq5a8n45x6qjcGgasm2ZoEe6HQKnw9qzAsLD1gM\nZ/Zzd7DolWwb6o27g7U2cmJ63whiEjOvjoR6IIAu4T7sSMhgZJsgHGysKC0zMLFrGI62ega3CLDo\n0TTvmba9zhzF7hE1tOu8SYSvK691D9MSF9Wcbal+k9ty2FnrtRFQYJyCc+3qquM6hnCwPPFVzdkW\ng6qSnlusBeY3Y7oXbIewajQNcK90sbMhLQNxtrNmUHN/iwVnnmtXm6UHUjmQlI2NlY6arnY83TaY\nYa0CAXgksibZBcaezVOXcrUkvIejDZ5OV8+vwS0tF3BRFIUZj0VSWFJG2BtrLF4zXd9N1+QJXevy\n+aYELWFsuu6CcQ7y022DmLs1UUuCj2lfmxpudtoicWAc7XDywtW1Onzd7anr48yauPM421lpyaeo\nQA983ey1XmxT4m1Q81oWt80wPwfN51+DcREdVJVXZlT4mK9L+TvdeNa2Roja5+3vsLHSs+XkJab2\nDqehUx6Kuy96ncKcLYkkXMxBp1OwtdJVmhUyZ1BVVBWU8hUoi8sMlJQasNbrsNIr6BSF+jVdeLNn\nuMV78ovKcLDVa/t3cnJix44dTJ06lbc/+pJ+3doz4a3pLJn/H35ftYr58+czYcIEfH2Nwcz48eMZ\nPHQoBw4eZsgTA/n888+ZMGECu3fvxsam4nL2x44do149Y0ReUmZg31njZOHbWeHuzzqUko2vm32l\ny6QeS7vCoj3JzN9xBjtrHbOfbMKI+cZenNe6h5FfXKZNfm1Sy42lY1rf8FimRWsa+LrS8d/ReDvb\nElbdRQvyTIGM6f/bJra3qCB/ikni1aWH+fKpJnRtcP3l2MG4BOyFnEKaXSfzaH6vs/882YRang54\nO9vecGl/U0BguvcPwJoj5xn9wz6+Gd7MogI9knqZ/OIymgW6a3+DaQERMM53GNS8VoVVxpIy8ikx\nGLTA8EbyikqJOZNJ/RouN7wP0+X8Eg6lZvNAkKf2m0rKyKfUYLilleh2nspg0Bxj4mLDy205mpbD\nuIUH+OmZFrc9rvtm9p3NwtvJllqeDlpDfVyHOlrvkqqqvLDwAL8fTuPrYc1QgYZ+bsRfyCHI25GL\nV4oqXTXytWWHWbY/lQNTOmNnrefdVUeZszWRBaMeoHX5CoW34vj5KxQUG1dhqyz433c2k8ISTpnG\nhAAAIABJREFUAw8EeVQIdL/acor3fj/O4mdb4mxnhaIYA54arvYUlxo4kJSFk50Vj3y2DWu9Qvy7\n3S0yvAenPMz+pCzCfV1u+Du9VXlFpRxNu8Lry45w4kIObUK8GPlgEN7OtpUOLzUXfyGHzuWBHFhm\nFW+kpMxAyGRjj//Po1vSLNCD0d/vsxi6aPJUi1r8sCuJPo19ebSxLz/FJLHu6AWWj2mNg62e2t5O\n2kIFAIffeviO7rv54IxNXLhSyPZXO9zy5/vIZ1s5m5HP9okdKtym5Xpqv/a71tiobFGO/UlZBHs5\nVnpPy4s5hZX+xjcfv8jw+XsqHR1hMKjsPZtFA18XixUPzb+L59vXoWfDmhYBmsngebtJTM9j28QO\nPPzxH2TmFfPNsOYEeDkQ+ZYxabb4WeNCKnPLR0+Y5quZ5BSWEFG+7Zn3H6n0c1FVlZjETGpXc7rh\nvae2nLykDVvf93qnSq9dcecuM3bBfs5k5PNO73AGl8/tNn/v3tc73fY9rvrO3q4tZOBsa0XM5E63\ndO/GuHOXb3p9+TspKi0jNimbpgHut7zqren6WNn3eymniDVH0njj1zi6hPvw38FRFbYxeWtFHPN3\nnMHNwZrtEzvcdCVKc3lFpTSdtp4AD0ft1hqlZQYe+jCa1OwClo1pRXGpgca13FEU2H82C71Ooba3\nE9kFJbSfGQ1A4vTuFJYY2J2YQaiP823fu660zEDjd9bjaGOljYS6l8zbFttf7VDpfWM/2XCSTzbE\nM29oFB3CqhGTmEmkn9st/X5zCkvYe+bPX3ue+2GflvzvHlGd2U82ve62b/8Wx8KYJHa/1glXe2ti\nk7MpM6g3vOdhq+kbqePjzLgOdSgsMbA8NpVf9qWwdEwrbb6kqX5xtLW6o1s2/Lw3mQm/HKK2tyPj\nOoYw/qdYnG2tOPx2F22bxPQ8EtON6yvc6LYSpnPmevdkVBRln6qq1z9ZzLf9OwVz7gFhatT4/wLG\nLOvcIVGcTzqFnVctPJ1s+HRDPHFpV/izC1uXlBm0JYFNvRDXBnOVcXJyIjc3l6ioKJ4Z/Rz7Dx+j\na5eHmTv7M1auXMn8+fPZu3cvs2bNqvDe9957j6lTp7Jz504aN648W2sezP3d7DqdwcCvdtEy2JOF\nz7SgxXsbOX+lkGmPNiDC11Wb+H/qve43vJ3BtUrKDMYl4xW0IVemiflLnmtJhK9bpcFsUWnZXbsf\nVGFJGaUG9ZZv8P7N9kS2nLzE3KHNLP7WWy1TcmY+Y3/cj05RmDMkqkIvxd9Vem4RUdM2AFcv1Hfz\ne7iewfN2szU+ncnd61W4V5n5sta3QlVVissMWplNc1Bv5f5bd9PNPrei0jJGzN9Dj8iaDGpunIsy\n/qcD1PJwuG4m/E59sTmB3w6e47Xu9bSeu1tRWFJGwsVcJi09zORH6t1yYP/OyqMUlJTxXh/jUCGD\nwbiEtKIY71O572wWXzxhXAbd/Hu+9jsEYyPx6e/24u1sy1eDm97RbQ+uXeL7Vph6QW+1wQvQ6aM/\nSLiYS0M/V5aOaX1b9eaN3O45Aca5pN/uOMO8Yc20XutrlRlUDKqqLYOuUxStzKbGyIaXH6JOebb7\neuUYt/AAgZ4OWmLmz8rILWLUd3txd7BhzpCo635+BoNKXnGpRYCvqipjf9xPcanKV4ObVno7mxtZ\nvCeZb3eeYUa/SOpWd75vNwj+O7pRMGdSUH5blBt97qpqXFDMzlr3p64xRaVl6BXF4pwsMxgXzbvR\n+VFaZmD8T7GMahN03Z7x22G6LdFf8RtJu1zA6O/34e5ow7xr2ifm8otL//JrHsDEXw6xqHyee2UJ\nJ3OV1fM3U1JmQG92C6J7eX1PuJjLS4tiGdDMn3Z1vRmzYD9dwqtX2oN8M1N+PcKJ8znMH9680qC6\nygZzUVFR6t69ljfvvJuBTkmZgfScIrycbLG+jV4vUzA3depUPv30U6Kjo8nIyGDmzJk3DeYGDRrE\n5s2b+fbbb+nSpUsle/97B3OFJWV8vP4kfZoYb3zbavpGzl0u5OMBDekRWZOZa08Q4ed60xs+3siy\nAykUlRho6O/Gr7HneKlzyD0PFMStM90QNbymC+3u4Oa4t2vcwgOsOHjuukNlhaiKDiRl0Wf2Dvo0\n9uXj8mFyVdXivckkZeTzcufQ2w6MxP+W6BMXsbHS0ar2rY90EP8MH6w5zuzoU7c8rFMY3U4w97eb\nM3cvWet12gT0P2PEiBG4ubkRERFBdHT0TbdfunQpmZmZbNmyhR49ehATE4Ob243Hqv/d2FnrLYZP\nNQ5w59yhNGq42mOt193S0KqbMb8Fwo3mrYn7Q1GUP5V1ulOvP1KPTvV96Gx2E10hqrpG/m7MGRKl\nrfhXlT0uSRZR7q9M9Imq5ek2wdSt7qytzCruPhkjcBv8/PwYN27cLW2bnp7Oq6++yty5cwkNDeX5\n559n/Pjx97iE994nAxqxa1LHuz5XSohrVXOx05YnF+J/haIodK7vU+lcLyGE+F/jXr4c/63OKxa3\n7x81zPLv6p/wNwohhBBCCCFu7naGWUrPnBBCCCGEEEJUQRLMCSGEEEIIIUQVJMGcEEIIIYQQQlRB\nEswJIYQQQgghRBUkwZwQQgghhBBCVEESzAkhhBBCCCFEFSTB3C1QFIWnnnpKe1xaWoq3tzc9evQA\nYP78+Xh7e9OoUSMaNWrEkCFD7ldRhRBCCCGEEP8QVve7AFWBo6MjR44coaCgAHt7e9avX4+vr6/F\nNgMGDGDWrFn3qYRCCCGEEEKIfxrpmbtF3bt3Z9WqVQAsXLiQQYMG3XD7U6dO0aRJE+1xfHy8xWMh\nhBBCCCGEuBNVq2du9atw/vDd3Wf1COj2/k03GzhwIFOnTqVHjx4cOnSIESNGsHXrVu31RYsWsW3b\nNgDGjx/P8OHDcXV1JTY2lkaNGvHNN98wfPjwu1t2IYQQQgghxD/WHfXMKYrSX1GUOEVRDIqiRF3z\n2iRFURIURTmhKEqXOyvm/RcZGcmZM2dYuHAh3bt3r/D6gAEDiI2NJTY2VgvaRo0axTfffENZWRmL\nFi3iiSee+KuLLYQQQgghhPgfdac9c0eAvsB/zZ9UFKU+MBAIB2oCGxRFCVVVteyOjnYLPWj3Uq9e\nvfi///s/oqOjycjIuOn2/fr14+2336ZDhw40bdoUT0/Pv6CUQgghhBBCiH+COwrmVFU9BsbVHq/R\nG/hJVdUiIFFRlASgObDzTo53v40YMQI3NzciIiKIjo6+6fZ2dnZ06dKF5557jnnz5t37AgohhBBC\nCCH+Me7VAii+QLLZ45Ty56o0Pz8/xo0bd1vvefLJJ9HpdDz88MP3qFRCCCGEEEKIf6Kb9swpirIB\nqF7JS5NVVf31TgugKMozwDMAtWrVutPd3RO5ubkVnmvXrh3t2rUDYNiwYQwbNqzS927bto3hw4ej\n1+vvYQmFEEIIIYQQ/zQ3DeZUVe30J/abCvibPfYrf66y/X8FfAUQFRWl/olj/W316dOHU6dOsWnT\npvtdFCGEEEIIIcT/mHt1a4IVwI+KonyEcQGUECDmHh3rb2vZsmX3uwhCCCGEEEKI/1F3emuCPoqi\npAAtgVWKoqwFUFU1DlgMHAXWAGPveCVLIYQQQgghhBCaO13NchlQafeTqqrvAu/eyf6FEEIIIYQQ\nQlTuXq1mKYQQQgghhBDiHpJgTgghhBBCCCGqIAnmboGiKDz11FPa49LSUry9venRowcA8+fPx9vb\nm0aNGtGoUSOGDBlyv4oqhBBCCCGE+Ie4V6tZ/k9xdHTkyJEjFBQUYG9vz/r16/H1tbwH+oABA5g1\na9Z9KqEQQgghhBDin0Z65m5R9+7dWbVqFQALFy5k0KBBN9z+3LlzWk9do0aN0Ov1nD179q8oqhBC\nCCGEEOIfoEr1zM2ImcHxzON3dZ9hHmFMbD7xptsNHDiQqVOn0qNHDw4dOsSIESPYunWr9vqiRYvY\ntm0bAOPHj2f48OHExsYC8MUXX/DHH38QEBBwV8suhBBCCCGE+OeqUsHc/RQZGcmZM2dYuHAh3bt3\nr/D69YZZbt++nTlz5miBnhBCCCGEEELcDVUqmLuVHrR7qVevXvzf//0f0dHRZGRk3HT7tLQ0Ro4c\nyYoVK3BycvoLSiiEEEIIIYT4p6hSwdz9NmLECNzc3IiIiCA6OvqG25aUlNC/f39mzJhBaGjoX1NA\nIYQQQgghxD+GLIByG/z8/Bg3btwtbbtjxw727t3Lm2++qS2Ccu7cuXtcQiGEEEIIIcQ/haKq6v0u\ngyYqKkrdu3evxXPHjh2jXr1696lEf41/wt8ohBBCCCGEuDlFUfapqhp1K9tKz5wQQgghhBBCVEES\nzAkhhBBCCCFEFVQlgrm/01DQu+1/+W8TQgghhBBC3Dt/+2DOzs6OjIyM/8mgR1VVMjIysLOzu99F\nEUIIIYQQQlQxf/tbE/j5+ZGSksKlS5fud1HuCTs7O/z8/O53MYQQQgghhBBVzN8+mLO2tiYoKOh+\nF0MIIYQQQggh/lb+9sMshRBCCCGEEEJUJMGcEEIIIYQQQlRBEswJIYQQQgghRBUkwZwQQgghhBBC\nVEESzAkhhBBCCCFEFXRHwZyiKB8qinJcUZRDiqIsUxTFzey1SYqiJCiKckJRlC53XlQhhBBCCCGE\nECZ32jO3HmigqmokcBKYBKAoSn1gIBAOdAVmK4qiv8NjCSGEEEIIIYQod0fBnKqq61RVLS1/uAsw\n3f26N/CTqqpFqqomAglA8zs5lhBCCCGEEEKIq+7mnLkRwOry//sCyWavpZQ/V4GiKM8oirJXUZS9\nly5duovFEUIIIYQQQoj/XVY320BRlA1A9Upemqyq6q/l20wGSoEFt1sAVVW/Ar4CiIqKUm/3/UII\nIYQQQgjxT3TTYE5V1U43el1RlGFAD6CjqqqmYCwV8DfbzK/8OSGEEEIIIYQQd8GdrmbZFfgX0EtV\n1Xyzl1YAAxVFsVUUJQgIAWLu5FhCCCGEEEIIIa66ac/cTcwCbIH1iqIA7FJVdbSqqnGKoiwGjmIc\nfjlWVdWyOzyWEEIIIYQQQohydxTMqapa5wavvQu8eyf7F0IIIYQQQghRubu5mqUQQgghhBBCiL+I\nBHNCCCGEEEIIUQVJMCeEEEIIIYQQVZAEc0IIIYQQQghRBUkwJ4QQQgghhBBVkARzQgghhBBCCFEF\nSTAnhBBCCCGEEFWQBHNCCCGEEEIIUQVJMCeEEEIIIYQQVZAEc0IIIYQQQghRBUkwJ4QQQgghhBBV\nkARzQgghhBBCCFEFSTAnhBBCCCGEEFWQBHNCCCGEEEIIUQVJMCeEEEIIIYQQVZAEc0IIIYQQQghR\nBUkwJ4QQQgghhBBVkARzQgghhBBCCFEFSTAnhBBCCCGEEFWQBHNCCCGEEEIIUQVJMCeEEEIIIYQQ\nVZAEc0IIIYQQQghRBd1RMKcoyjuKohxSFCVWUZR1iqLUNHttkqIoCYqinFAUpcudF1UIIYQQQggh\nhMmd9sx9qKpqpKqqjYCVwBQARVHqAwOBcKArMFtRFP0dHksIIYQQQgghRLk7CuZUVb1i9tARUMv/\n3xv4SVXVIlVVE4EEoPmdHEsIIYQQQgghxFVWd7oDRVHeBYYAl4H25U/7ArvMNkspf66y9z8DPANQ\nq1atOy2OEEIIIYQQQvwj3LRnTlGUDYqiHKnkX28AVVUnq6rqDywAnr/dAqiq+pWqqlGqqkZ5e3vf\n/l8ghBBCCCGEEP9AN+2ZU1W10y3uawHwO/AmkAr4m73mV/6cEEIIIYQQQoi74E5Xswwxe9gbOF7+\n/xXAQEVRbBVFCQJCgJg7OZYQQgghhBBCiKvudM7c+4qi1AUMwFlgNICqqnGKoiwGjgKlwFhVVcvu\n8FhCCCGEEEIIIcrdUTCnqmq/G7z2LvDunexfCCGEEEIIIUTl7vQ+c0IIIYQQQggh7gMJ5oQQQggh\nhBCiCpJgTgghhBBCCCGqIAnmhBBCCCGEEKIKkmBOCCGEEEIIIaogCeaEEEIIIYQQogqSYE4IIYQQ\nQgghqiAJ5oQQQgghhBCiCpJgTgghhBBCCCGqIAnmhBBCCCGEEKIKkmBOCCGEEEIIIaogCeaEEEII\nIYQQogqSYE4IIYQQQgghqiAJ5oQQQgghhBCiCpJgTgghhBBCCCGqIAnmhBBCCCGEEKIKkmBOCCGE\nEEIIIaogCeaEEEIIIYQQogqq8sFcXEYcmYWZf8lxtqdup6is6J4fS1R0uegyO87toLis+H4XRQgh\nhBCiyik1lLIrbRcns07e76KIu6hKB3PZhdkMXDmQlza/dE+Ps+f8HgauHMjoDaNZfGLxPT3WrSou\nK2bu4bmcvXL2fhflnlNVlSd/f5Jn1z/Lb6d+A2BZ/DL2nN9z147x88mfOXDxwF3bX2V2p+1m5emV\n9/QY4t5KzU3li9gvSMlJud9F+Z9Xaihl7uG5vLH9DbambAXgVPYpZsfO5lL+pftcOkgvSGfOoTlc\nLrp82++NvRjLT8d/AsCgGvg27tsKjauErAQ+2/8ZaxLX3JXymruYf5E5h+aQU5xz1/d9r5WUlTDv\n8DzOXD5zz46x8exGNiZtvGf7vxOqqrLg2AJ+P/37Xd1vam4qn+3/jMUnFqOq6l3dt7l9F/bx6f5P\nOXjp4D07hri+P5L/4Ol1T9NvRb8/nRxfFr+M5QnL73LJ7o41iWvYlrrtnh5DVVV+Ov4Tq06vuqfH\nuR1/q2AuKSeJL2K/wKAamLxtMj8e+/GG26flpQGw/+J+CkoLeHHzi0QnR9/VMiVfSWbE2hHa4w/2\nfEBcetxdPcafsff8Xj7d/yk9lvW45Yr3SPoRRq4dyfhN4yksLbzp9rEXYxmxdgRvbH/jrlfucRlx\njFo7ij+S/7jptim5KVrQmpyTzPbU7UzZMYUJf0y443Kk5qby2IrHmLpzKs9teO6O93cjz6x/hklb\nJ1n07r4f8z5DVw/V/o1aO4r4rHiL921N2cqotaM4kn7klo91JP0IYzaM4XzeeQBSclJ4dv2zt3R+\n5BbnMm7TOLakbLnl4/2VVFVl6s6pDFszjJ3ndt5w2w/2fMDQ1UMZtmaYxd/+++nfGbVuFKcvn77p\n8b6L+45pu6ax5/weui7pypcHv2Ti1omM2TCGC3kXKj3mM+ueIflK8m3/bX9Gfkk+4zaNu6VzyeTb\nuG95e+fbFuf1/gv7GbtxLOkF6Ry+dJiRa0cycctEygxlN9xXmaGMSVsn0XdFX97b/d4Ntz175Sxj\nNoy5pazwgYsH+HT/pyxPWM6YjWMA+O+h//Kfg/+hw88dOJpxFDD22o/dOJZv47696T7vpl8TfuWz\nA5/xUvStJxPj0uMYuXYkg1cP5t3d75Kam8rRjKPM3DuTfiv68cjSR0i+kkxyTjJ9VvRhzuE5vLbt\nNUoNpbdVtvSCdEZvGK0FjObyS/Lp+HNHPjvwGZuTN1d4/fClw4zeMPovSRReyr/EmA1j2H9hP9N2\nTeO1ra9hUA03fM+e83v4ZP8n9Fze87qfy4W8C4zdOPa26kyTNYlreDH6RV7c/OJtv/evsDR+Ke/H\nvM/ErROJvRhLWm4az214jtiLsZVuvyZxDaPWjeJYxjEm/DGBFadWVLrdLyd/Yc7hObyz6517mnSc\nuWcmcw/P5ZN9n9yzY/wZZYYy3trxFscyjlV47eClg4xaO+qeBwl/hXN557T/rzlz64miXWm7GL5m\nOANXDmTKjim8sf0N8kry7kUR/5Tc4lxe2PgCE7ZMuGdtuY1nNzJ09VDaLW7Hu7vf5dWtr/5tRotZ\n3e8CmMspzuHLg1/SL6QfK06tYMWpFYR7heNh64G/i7+2XUlZCdEp0bwc/bL23BcHvmBjkjGbtvnx\nzaiqireDN2DMcOaVGn90vk6+eNl7se7MOl754xUAHKwcmPbgNMLcwyyOE5cex8BVAwF4s+Wb5BTn\n8NG+j1h3dh02ehvquNVBURTO553nQv7VRp2t3paisiLs9HZcKb7C2I1jKSgtAECnGOPnfiH9mNJy\nCgCbkzbzUvRLlKll2OhsKDYUY6e3Y3qb6dRwqkGYexh6nZ6P933M10e+5omwJ/Cy99KOdzTzKOGe\n4by14y22pGxh+aPLcbFxsfhsNydtZtzmcdrjU9mnUBSFEkMJVooVYR5hFBuKic+KJz4rnukx07Wg\nYw976BncEzsrO6x11ozZOIa8kjy+7fot9TzrWRzHoBo4lX2KYNdg9Dq99nypoZSzV86y4tQKfjz2\nI4VlxmBy9/nddA/qzpD6QwjzCKNMLSM+O55Qt1Cs9dYAZBRkaPuZd2QeKbnGXhFT+c7nncdGb4OH\nnYdFWQpLCzmXe47LxZcZtXYUk1tMpm9IX/JL8kkvSEdF5fuj33Mi6wQAeSV5bEvdxoO+D2r7KDOU\n0XdFX85cOVOhkVHNoRor+6zE3sreeKy8cwS7Bmuvq6rKqHWjiDkfw+D6g7X3N/uhGQD2Vvbkl+bj\n7+xPDcca2uex+MRiJreYbPE377uwj0GrBmGrt2V6m+lEeEVQ3bE61/PLyV/YmrqVxScW07N2Tyb8\nMYETWSdwsHKgnX87ABYcW8D7Me/TskZLDqcfZlrraXQM6MiMPTPYnLyZzcmb0St6mvg04e1Wb3M8\n8ziTt02mZ3BPnm/8PLZ6W+Kz47FSrKjrURcrnWV1YlANJGQnYFANeNp5auejSdKVJAasHEB+aT7d\ng7rTs3ZPxm0aR3FZMXXc6zCn8xxSclOw0lkR5h5GdlE2mYWZfH/0e5YlLAPgo30f8YPPD9jqbZkR\nM4ONSRtZ2WclNnob4rPi+f7o9/g6+ZKam8q+C/uY33U+2UXZTNw6EYDey3vTp04fhoUP4/Xtr5Ne\nkM7sjrMxYGDo6qH8q9m/+HDvhwAsOrFIK/uhS4cAmLx9Ml92+pLEy4nUcKzBG9vfYEPSBgDWnV3H\n90e/J7MwE18nX95v+75Wzv0X92NvZc/CRxaionL28lnt/NQpOqwUKz7v8Dk5JTm8uvVVDKoBL3sv\nOtXqxOKTi5n+4HRC3EMoMZRw8OJBNidv5uClgyzttRRPe08MqoETmSf4+sjXxJyP4dfev+Jm56aV\nf+bemQAsj1/Ox+0/ZmPSRi3T2n5xex7ye4iY8zEA/F/U/2FvZU9WYZZWP34R+wXfHPmGYeHD+O+h\n/2r7jc+KZ0zDMdqx4rPiyS/NJ8A5AFsrW76L+46tqVuxs7LDwcqB1Ymr+aDtB3yw5wPO5Z3DzdaN\nT9p/gpXOite2vWbxe9mWuo3Viau1xxvObqC+Z30OXTrElpQtbEnZwpD6Qzh75SzVHKphb2XP8czj\n+Dv742TjpL0vuzCbhScWMu/wPL7q/BVNfJpQaigl8XKiVqebFJcVcyLzBN4O3hbnW0JWAicyjfXG\nnvN7mLhlIk/Ue4KajjXxdvAmJSeFjMIM7K3sKSgtoJZzLax0Vsw5PIeY8zFY66wpMZTQdUlXrJSr\n501SThLdl3XXHtd2rc2py6dotbAVX3X+Cp2io65HXWz1tlzKv2TRMDNd2wDWnVnH9tTtbE/dTreg\nbrjaugKQlpvG/ov7LX7HF/Mv8vXhr1nUcxH+zv488fsTAOw8t5MAlwAqU2oo5fTl04S4hVBQWkDP\n5T0J9wxnZMRIgl2DcbZxvuF7FEXhP7H/YfbB2QDoFT3RKdGAMXn3StTVa3MdtzqsPbOWydsmY623\nxsn66nfZ5Psm2OhteMjvIV5s8iKZRcYpF6bfg6edJw28GvDOzndYfWY1Gx7bQHZRNhkFGVjrrXlx\n84tcLrrMqr6rOJd7jjK1jB+O/aDtP+LbCGx0NrzZ6k16BvfUfhsZBRmUGkqJOR/DlO1TUFF5scmL\nNPZpjIetB0PXDKVX7V682PTGAeGp7FN42HlQppaRW5xLoGugxevjNo0jOjmaD9p+QLBbMP7O/syP\nm6+9Pnj1YO3/21K3sbbfWgpKCxiwcgAD6w6kb2hfJmwxJj0fX/k4ANHJ0QS7BlPXoy7WOmvt/VmF\nWVrb5bVtr5FTnEOXwC542nsCxiRAr+W9uFRwiT51+tCiZgve2/Uen7T/hCY+Ta77NxaXFXM88zi2\nelsSLydyJMMYYO+9sJeNSRvxdfLFz8mPrKIsbHQ2ONk4kXQliRD3EI5nHmf85vFkFGQwqfkkBoQN\nuO5xCkoL2HdhH69Ev0KpoZQJzSbQvEZz7Zp8Ie8CvZb3oppDNZb3Xq61TwpLCzmZdZJzuedYEr+E\nJfFLWNVnFbVcalFiKOGFTS+wPXU7YLw+m0xtNZVI70hyS3KvWyYw9oJP3jaZ4eHDea7R1SCjpKyE\nhOwE6nrU1dqFI9eO5OClg3zc7mNcbF1wt3WnlkstrRfa9PswtTkDXQJxtXXlZNZJnKydqOlU84Zl\nySjI0OotgMnbJhPpFWnxuzPt29XG1eL5DWc3cPDSQUoMJRbv/6T9nwvK80rySM5Jpq57XYs691Zl\nF2aTUZiBo7Ujdno7TmSd0OoQgB+P/cgT9Z64pX2dyj7Fk78/yestXuejvR8xosEInqr/lMU2U7ZP\n0dod5potaMbmxzdXaH+CMWlqutYGugTyYpMXmbBlAp72nqx4dAUvbX6JPef3sKLPCq4UXWHE2hE8\nFvoYnQI6EeBced17Pcrd6HFRFOUVYCbgrapqevlzk4CRQBkwTlXVtTfbj32QvVrnrTp423tzqcBy\nGM2oiFEMCx+Gq60r4zaNqzSjaM7Zxpkdg3ZwPPM4/X/rrz1vpVgxrMEw5h6eW+n7tg7YqjVEFh1f\nxLTd03i1+as8We9JADos7qCVbULUBJr6NNUCvlvxTOQzbEraRJlaxgdtP2B32m62pGzRGk6Veavl\nW/QL7cfQ1UO1C7GjtaOWFQl2DWZ2p9l0XdIVgOcaPseYRmMs9vH5gc/56tBXPB3xNHMOz6Gue10t\niAEYUHcAxzOP39bQh0jvSD5o+wFnL58lPjseT3tPHK0cGbd5HL5OvgwKG4SjtSNe9l6RvdTkAAAg\nAElEQVSczDrJ5wc+v+H++of2x8vei/8c/A+dAzrTxrcN/s7+HM04yod7P6RZ9WYVhlaOazyOzw58\nRqh7KEt6LbF47fHfHudY5jGtQWWlWPF84+f5ZH/FyqdrYFctSzW8wXD8nf3pW6cvsZdiGbZmGMGu\nwZX24izttZQQ9xDe2fkOi08u5qN2H9E5oDMA03dP58fjFXuXn4l8hrj0OLafM14gpraaSp+QPgC0\nW9SOvJI8lvVexsakjfg4+GgX4/6h/fn55M/aftY/tp7qjtUpMZSw9ORSCssKifKJ4mjmUZaeXKpd\nNM3Z6m2JfjyaJfFLtErGpEtgF2Y+NJNRa0dZXLQqE+4ZTqh7qFa59anTh6mtp2qvJ15OZNquadrv\n2tPOk439N6LX6Vl1ehWh7qGsPL2Sr498TZBrEImXE7X3utq6Vhi61qpmK3ac26E9ttPbEekdScz5\nGAJdAhkYNpD3Y94HYGWflRzNOMq/tvwLgDdavEFGYQazY2db7LNvSF+WxS9DpWId2LJGS3amWfb6\nudu609avLSeyTnA88zhwtQF9o/PG086TjMIMi+ecbZzJKc6hU61OWvBnMipiFPOPzCeqehS13Wqz\n5OQSOgV0uqVseV33uvzS6xfWnFlj0XP9VL2neK7Rc7jYuFBUVkTUD1E33ZfJK01f4ZP9n1CmlrFt\n4DbSC9J59NdHr7t9O/92fNzuY97b/Z72e23o3ZD80vwKvc5gvMiduXLmlsvTL6QfS+KX0NC7Ia1q\ntiLxcqJ27poC9yDXILoHdeeL2C9wtnbm2YbPEuwaTIh7CF2WdNESK5FekSx4ZIF20e0R3IMOtTpQ\n06km4Z7hjN04li0pW3C2cWbrgK3odXpWnl7JpK2TtOPll+STVZSllc9Ux5qz1duiV/Tkl+YDEDvY\nOOrBVJ9Paj4JD3uPCqMNNvXfxORtky1+iy1rtGRmu5m0XtjaYttazrVY1dc47Kf/b/2136iVzop1\n/dZRVFZEt6Xdrvu5fvjQh2QUZGjnUW3X2izrvUxraK1OXM3ZK2ex1lmzLGEZZ6+cZXTD0XSs1dHi\nGgvGBMC1licsJyE7gWcjn8XN1o0Ze2ZctyzmHq3zaIUhXc42ztjp7Sq0E65V27U2yx9dTsS3EQB4\n2XuRXpB+02Oarhk+Dj5aovapek8R5hFGqHuoFhg52zijU3TY6GwqLcvBIQe1hvrhS4eJvRRLt6Bu\neNl7EZ8VT98VfS22HxQ2iACXAHrW7ole0dPixxaVlq9LYBfa+Lbh9e2vAxDqHmq8xnb4nCUnl1g0\nasFYfzbwasBXh77SnqvnUY9Hgh/RHpt67CY2m8jIdSO151f2WYmXvRdzDs1h3pF5OFo74m3vbXHO\nrn9sPZfyLxGXEUefkD7Y6m211z7b/1mF8+HLTl8yesNo7bFO0WnnpIedR6XrIOgUHav6rMLP2c/i\neVVV+e30b8yOnU1qbmqF9/UP7Y+brZtFGSK9I3k44GHCPMKITo62COABetXuxbjG41hzZg0z986k\nhmMN+tTpQ0J2AuvOrgOMddrtDhX9uefPhHmEkXwlmdEbRpOUk0S3oG580PYDVFUl8rtIi+31ip4X\nGr+gtVn+2/m/tKjRgtYLW5NbkoujtSMda3XUvrtVfVaRlJPEqexTdA7oXCG4e2zFY5zIOoGfkx/D\nGwznnV3v8EHbD+gWZKwXNiVtYvzm8drnvbbfWpJzkik1lPLzyZ9JyE5Ar+hJyE7Q9jkhagLdgrpp\nydrViatxtHbE2caZQ5cOEeIWQivfVgCczj7N1tSt2OhtmHVgFleKr9A5oDMNvRvSKaATyTnJnMg8\nQTv/dhUSSbEXYzl9+TTdg7rza8KvTNs9zeL1KJ8o9l7Yqz221duybeA27Kzsbvq9/JrwK69vf92i\nLbKg+wIivY3fR0xajHZOmBIeTX2aYm9lz7bUbThYObBt0DbOXD7DjnM7yC/Jx8HaQavzTOp51ONY\nprHnd2j9oXx71DiapJ1/O9Jy0yza5E19mvJtt2/3qap6SxfrOw7mFEXxB+YCYUBTVVXTFUWpDywE\nmgM1gQ1AqKqqNxyvExoZqtq+crUSmNJyCgaDweJLq+ZQjYv5F6nmUI1prafhYuuCXtFXuJgA9Aju\nwcFLB0nOSWZ6m+kcyzjGd0e/015/o8UbNKrWiHGbxmmVwE+P/ES4VzgG1cCDCx8kpySH2MGxWhbn\nhU0vVDpU7emIp2ni04Qd53bw/dHvK7z+U4+fqO5QHU97T2bEzKhQeZhzsXFhdqfZ5BTn8K8//oWH\nvQejG47my4Nfcj7vvNYj1c7f2PDfc34PAS4B2rAYBysHdj2xyyLbMXXnVDYmbeTbrt/Sc3lP7fnZ\nHWdrQ5gA/Jz8KC4rpsRQQnZRNhFeERzLPGaRjZnWepp2EbnWtQGHiamRBRDgEsCUFlPYlLyJBccW\n8GHbD7WA5VoOVg40r96c6JRo/hjwBysSVvDvff+udNsJURMYEj4EMGaXOv/SudLtrtXOrx2fd/zc\norcWwN/Zn5ScFFRUPu/wOeM3j6eOWx2LIWL2VvaMaTjGokyD6w8mLj1Oa6iZBwZD6g9hQrMJqKrK\nU78/RVxGHAsfWaj1cJp+G9cG2+89+B49a/fk7Z1v88vJXwB40PdB7K3siUuPs8jQm9Rxq8Pg+oN5\nc8ebwNUAItwznLiMyocKbxu4jWFrhmkVUJhHmNYoBGPQVlhWyPoz6ylVS6njVkfbtnG1xlp2qrL5\nJrM6zOKbuG/Yd2GfxfPmv6e3W71Nz+CejN04lp1pO2nq07TC9o2rNWbmQzPRK3qe2/CcVjmaNKnW\nxKL3YUH3BVRzqEaPZT1wsXFhauupuNu6E+4VXqGhMb3NdK2hbhLuGc6LTV+koXdD7K3sOZV96obB\nzLjG4/ju6HdkF2UDEP14NAnZCSw6sYj1Z9czsdlEugZ1pf3i9hbvc7By4Jeev+Dv4k/v5b215EFt\n19rM7TK3wvYmT0c8TbPqzfjt1G+sSlxFe//2nL58mrTcNKa2nqoFtQ/UeIC5D8/VAr2JzSYy78g8\ni8Ztt6BuWu9XI+9GxF6yHLr1oO+DnM87T0J2Au3923M4/TButm70C+ln0Tg3T7y09WtrMWTXw86D\ndx98FzDWp+ZD5aa0nKL1UisoBLgEkF2UzdiNY9Er+v9v777jo6rSx49/npAAIbSEogESacEEjETp\nuNRIUxARVBAVK7qwrmtDhR+6uu5XXaW5Iuoq2LBQVCx0EUGqCSTSA4QgJZRICCSkTGbO7497Z5hJ\ngSAgTHjer9e8MnNunZyZe+9zznPuMKnbJGLrxPLID4/4XLC6P9t/xP1X3c+xgmPFjltTe031SbH/\nS/2/UKlCJc9n+7XOrxFXN47KFSqz8feNLN2z1Kf3tntEd5bsWVLiNjcM20CBs4DEg4lEVo+kftX6\nAAz+brDPd/PXu3/FYEg8mEi+M5+nfnqKbEc2I+NGMjlpMrdE3UKPK3qwaPcivtz+Jf2b9GdM+zEM\nmDOg2IWtuzfQ7d0e7zJ9y3R+2lt6eu6YdmPoHtmdZ5c/e8oGR4CRcSNZuX/lGY09ntZrGl/t+Ipv\ndn5DTFgMU3tNJflwMgZDbmGuT/aNYJ3PDIZbm91Kx3odeWzpYzSt2ZTwkHCW71vObc1uo1uk9T15\n5IdHKDSFDI0ZyvQt00+7LxHVIhjdzuoNblGrBbuydhFbJ5bUo6kM+nZQqcu1C29H9YrVWbR7UYnT\nR8SN4Fj+Mc85/8HYB/n7tVaP2yNLHilxGXcwWZplty8jtHIoW49spU5wHVzGRfeZ3UucNyQohHm3\nzCO0cig5jhySDiXxn1/+U2LjZL/G/fi/Tv9HalYqn275lC+2fUG1itW4pu41LNu7jIoBFbn+iutZ\nuHuhz/f2/Z7vM2bFGA7kHCAmLIbY2rHcF3sfkxInkXgo0RPs5jvz6XlFT8Z1HUfb6W1P+R4BwkPC\neem6l1j822I+2/oZ10dez4RuE3zmSclMYeA3AwHrmPVUm6cYnzi+2HnDzftaBHyDx7ua38WCtAUc\nOnHIZ941d6yhSlAV9hzbQ9+v+/pk6TzT9plSe7Dn7ZrHNzu/oW/jvnyX+h23NbuNiGoRxa5h3AFz\n+0/b0+OKHtwSdQs7j+4s1uDa44oePNf+OTp90anEz8iw5sP4fNvnnmvE+Mh4wAoKR8SN4K65d9Hm\n8jY82eZJQiuF0uGzDrQPb8//ev4Ph8tB20/aUmgK6dOwD/PS5nFj4xs948KqV6xOVGgU/+n8H/Ye\n38vYFWP57fhvANzT4h6rES9xQokB7vWR15PtyGZ1+uoS/09gNdIt3L2Q4wXHqVmpJj/e9qNPtk/8\njHgO5R465fULwDvXv8PcXXOZs3MOY9qNYXD0YL5L/Y4lvy1hWIthtKzT0mf+6VumMytllk/QBVbj\n7bLBVg//yB9GAtb12/Crh5OSmULTmk2pWakmo5aNYn7afOqF1CvxOiw+Mp6bm97MY0sfo9BVyJWh\nV7L72G5Pdpq3ShUqMbHbRD7a9BGr0lex8Z6Nf2owNwv4FzAHaG0Hc88CGGNetudZAPzTGHPKAS6t\nW7c2d79rpcm83OllKlaoCFjd9K+ufZUZKdbNR6LDoply/RSfVMPpW6azav8qIqpF8NWOr3xyeRvV\naMSc/nMQEV5a/RIpmSlM6DrBkz5Q6Cpk8++bGTrX6n1rfVlrHrz6QR5a9BDRYdHM7HfyJO8yLnIL\nc5mQOMFz4nZfaLs5nA4W/7aYmSkziagWYY3x8eq1WJ2+mgcXPghYJ8t+TfqxMG0h89PmM7HbRCoG\nVPQEj+7USrBOZgOiBrDv+D6yCrIY1WYULuPigYUPANZJpWO9jkxInFCsyze7IJvI6pHM6DuDvy35\nG5l5mYxuN5q4unF8tvUzz1iXnwf/TLWK1XAZFwZDoATicDkQEWZsm8HK/SuZ1G0Sz698nm92fkOj\nGo2oXKEyNze9mZfXvmylDInVqrAmvXjvTrPQZoyIG0F8ZDzGGApNIUEBQaQeTaX/nP4lfi4CJIDO\n9Tvz33irZy/fmc/6Q+sZnzCee1rcQ63gWp7/QVjlMAIlkEO51sG4WsVq1K9an3ta3MPHmz8udhBo\nWaclo9qM8rTAfLL5Exb/thhjDMcd1sVh74a9GX71cBxOB0EVgnA4HRx3HKfLF1181uV9kqhZqSYR\n1SKY0HUC2zK3MXbFWIIDg/nXdf+izeVWmqUxhgJXgU8rZmmBwoohKzypsw6ng35f92Nf9j4CJZBG\nNRtRL6QetYJr8eX2LwGrBbBZaDMCJACH00GhKaTQVUjHzzp61tmnYR9e7fxqsdZAQRjUbBCj2ozi\nQM4BRv88mqpBVclz5vF6l9fZn72fET+M4HjBcdqHt+eZts949jkwIJBGNRoBcHuz262TUtbOEhtb\n4GSPnrvlfOltS6kVXAtjrIu54MBgxiWMI/lwMn+/9u9MWjeJkXEj6VCvg+d/eKLwBM+teI792ft9\neiNf7vQyPa7o4fn/FjgLqCAVfNJ/3dt5fOnj1K9an7EdxjJ2xVi+3vE19avWZ/ZNs6kSWKVYGki+\nM5+kQ0m8nvA6YZXDqB1cmyqBVRjVZhRBFYJIPpzMnXPv9OktcdedO3241cetKHBZ+fZtL2/Lm/Fv\nEhwYDEBaVpqn0WVI9BBGtxvN7JTZzNs1j1FtR/HCyhd4qOVDdAjv4FnfxoyNvLjqRQqNdZHVMbwj\nT7Z5EofTwU1f38Te7L3UqFQDh9PBicITJNyZQIAE8ONvP/LET0/Qq2EvXuv8Gh9v/pgFaQu4u8Xd\nPPmT1cMytddUJq6b6EkvjY+MZ2K3iThdTus4ERBIXmEeS/cu9fQuVQmswvLBy9mYsZFX1r5CSFAI\nE7tNpGpQVU8dTNs4jfGJ4wGr1bljvZOfT2/ucXvu5VzGxdxdc/lsy2e8eN2LRFaPJPlQMuMTx3NH\nzB2egPzhlg9zb4t7STuWxu3fWSlaXRp0YVzXcSQfSmb4ouE47TZGd7pz0aDl8VaPs3j3YnKd1oWT\nIDx49YP0btjbZ77UrFTGrhjLw1c/TNvwtmTlZ/HkT0/yQOwDzNkxhxxHDtUqVqNJzSY83PJhSuJ0\nOcl35vP40scJrxrO8x2e95nu3UIMeBoatx3ZxtPLnmZn1k7PtHuvupdH4h7hiZ+e8GSyPHT1Q1Sr\nWI3V6at5o/sbBAUEkePIYcj3Q9iVtYsACWDVkFUUmkJPz1/zWs3Z/PtmokKjPD2rbS9vS2T1SE/D\nEsCaO9aQcDCBd5Lf4YWOLxBeNdwzLceRQ/zMeM/rClKBJbctIaxymOc7HBwY7OnFcnt+5fOeY9ra\noWtZm76WyUmT+ds1f6Nzg87kFuZ6zpd5hXk+rfDevdOBEsjk+Mm0rNuSwIBAT89005pNmRw/mRqV\napS4fbef9/3sGYcTFBBE38Z9Cascxpr0NUzoNoGggCC6zuhKaKVQFgxagMu46DW7l0+Ggfviu2JA\nRQZEDeDykMuZtG6SZ/q6O9dR4CrgtV9eY/Z2K8skKjSKnlf0ZHX6atqHt2dy0mRPo4w3l3HR6pNW\nngCrV8NevHTdS55zuPsY4T1/SYFU0WPduIRxnrTOsMphLBq0iKRDSbyW8BoBEsCDsQ/y2NLHqBpU\ntdR0Q3fmxO1X3k6+M9/zf35z/ZusSl/FxK4TmbpxKgvSFhASFEKHeh0Y1WaUz7zGGJ5b+VyxHlpB\nPJkVM/vN9KTsOV1OnMaJIGz6fRMvrn6R3Vm7Gd1uNDc3vZk8Zx6fbf3M5/8PVsNfTK0Y+n/dnz3H\n9xBWOYyhMUMZfvVwzzwFzgLeXG81TALMvWUuEdUiKI37mD9gzgCfgGFs+7E0C23GXfPuIrZ2LK0v\na820TdM8mTo5jhxPz+zjrR5n3cF1/LzvZ8/x/ZVOr7Araxc/7/uZ17u8zsgfRhYL0MMqhxFWOcxn\nuyPjRnqOPz1n9SQ9J53P+37Oh5s+ZN6ueTzf4XluanITrT5p5bOuqNAoBkUN8qQurklfw8yUmew+\ntpvUo6mec5m3wIDAYuNaH732UZbuWUqz0GaeBrTqFatzrOCYz3zTek0jplYM7/z6DgvTFhZrnJp9\n02xPED8waiCbf9/MfbH30bthb4wx9PmyDxm5GYQEhfj09LqvjaNqRvFch+cY/P1gAiXQJ7vCzT3s\nCeCD3h/Q6rJWxeYxxvD40sfZfXw3gnBV7atIOZLCE62fIKZWjOc7le/Mp9BVSHBgMIWuQpIOJfHG\n+je4tu61/Lz/Z6JDo3nxuhcJDAjk9V9e58PNH/55wZyI9Ae6G2MeFZE0TgZzbwKrjTGf2PO9D8wz\nxswqYR3DgeEAkZGRrXbvLn3Q9fy0+WTmZTIkeshp980Yw3sb3iMrP4sRcSOoElTllPM7XU7iPo4r\nVj6r3yyuDLuyWPlvx35jZspMHoh9wDMe4Uws27uMHUd3cG+Le0+bL7w9c7sncLz9ytuJCo3ymT5j\n2wxCgkK4sfGNZOZl8u6v75Y4KLNjvY7EXxFfrPxI3hGmbZzG4OjBnhbiM1XoKuStpLfIys/iqtpX\nMSBqANsztzN7+2zm7JhDtiObdpe3471eJae3Amw9spVZKbPoWK8jSYeTOOE4wRfbvuDykMsZ12Wc\nJ+AqSXp2Oh9s+oACV4HnAiMwIJC1Q9f6jAuYnTKb4wXHGZc4jmvqXsNHfT4qbZWnlXAggelbplMh\noAKR1SL5a9xfGfjNQHZl7eKJVk9wz1X3/KH1vr/hfSaum0h0WDRtLm9D5wadaR/um24zMXEi7298\nn7g6cXx8g9UTvCNzBwO+sdI11w5d6wkMvK07uI5h84cRHBjM2qHWReuCtAUcKzjGF1u/YFvmNprX\nas6LHV8s8XPv5nA6mJI8hfjIeFrUbsGCtAXWTVfiRhTbrsu4uHf+vaw7tM5Kd+n5P2alzKKCVGBw\n9GAa1WjEqv2r2Pz7Zu6Pvb+ULZaNOzhwp1f9EdsztzMrZRZDoocUG8NSVk6XkynJU+jUoFOxlkC3\nt5LeYkryFB6IfYBHr3202PQuX3ThSN4REu9M9DRs/VFzU+d6xgne1uw2moU284w/yS3M5e3kt+nf\ntL/PmE+Hy8Hk9ZOJqRVDr4a9AOtYk5KZwsCogcXGy4J10d5tRjdyC3P5X8//FfvcFrVo9yIeX/o4\nYZXDWDhooU/Dxh9ljOHtX9/maN5RhrUY5kk1enrZ08zdNZeP+3xMXF3rWH+84DhTkqeQX5hPpwad\nPONJb/zyRk+r86c3fEpsndiz3q9zweFy8OzyZ1mQtoDqFauzYsgKz7SM3AxP7+3gKwdzR8wdNKrR\niOyCbN759R0GNB1A45qNS1xvjiOHd5LfoX/T/jSp2QQ4+fkEq6Fq/sD5zE6ZTUjFEHo37O3Tq936\nstZM6z3tlPv+6ZZPMRjSs9MZ1mJYsTG0JdmRuYPPt31O4xqNyzz+xe2E4wRvJb2FwTAibgQhQSGe\nacv3Lic1K5VhLYaVaV0FzgImJ02mSmAVhl89vMRz9rc7v6Vpzaae78WRvCOMTxjPsYJjNKzekBFx\nI1idvpp/rfqXp7ExUAJ5tt2zBAcG+zQIj1g8guX7lvN1/6899ZGRm8H7G96nZ8OeXFP3mmLb33Zk\nmycIHBg18JTH77IqdBXS5YsuHCs4xnMdnuPWZr6Ncu7vWsaJDAIkgEW7F/mklN/V/C5GtRl11vsB\n1k28hs4dWupPUXmntJbF4ROH+WjzRwyNGUpmXiaLdi9iRNwIAgMCPRkyr3R6xScV1a3QVcg1H1t1\n4O61Ox13nTYLbcbb179NnSp1cLqcdJvRjRxHDvWq1iPtWBo/3f6TJ+BYd3Adi3Yv4v7Y+9mfvZ85\nO+Z4OjWm9prqaRiGk9cNABO7TWRH5g7PZ9X7+O8etgPWZ8a717lmpZp8f8v3VK9Y3TNGzN1wV5oV\n+1aw5DcrA6HQFBJaKZTukd2Zu2suwYHBniFNQ6KHMDh6sM855svtX5KRm8G2I9tYuHsh1StW5834\nN7l73t1UCazi6aF3i60dy4aMDYCVtfDR5o84fOIwf437q8/3G6wxv4t3W0MYRITwkHD2Z1s9Zyv2\nr/AJDke3G0378PbMTpnN8JbDmb55umc8LxTvsDnfPtr0Ea8lvHZugzkRWQyUdKeFMcBooKcxJuuP\nBnPeWrdubRISEk41y3nl/vD2a9yPDvU6UKNSDTrV7/SHBmeqk1KzUtmUsYm4OnE+N5g5ndzCXFbu\nX+lJbyqr0ctH823qt56UxpKs3L+SJjWacFnIZWVeb1nsPLqTlMwUujToUqYDfGlW7V9FoxqNSr3J\nidPlZMmeJUSHRfu0Cu4+tpuM3IwSW5Dcth3Zhsu4il2MZ+VnkXAwgW4R3c7opFgWBc4CluxZQmS1\nSJrXan5O1+3thOMEP+39iWahzTwXQRer4wXHWbF/BR3CO5TYILQraxdZ+VmewONsOJwOftzzI7G1\nY316TM6HrPws1h1cR5eILqf9HDmcDpbtW0a7y9v53KTkfDiad5Tkw8l0btD5tMf0tKw01h9aT81K\nNeka0fWiOwcs37ucOlXqEB0W7VO+Jn0NEdUiTnsjhLLY9PsmBn9njQcvaRz2/F3zeWrZU9za7FYe\nbvkwdavUPettXgqmbpzKhMQJ3NX8LuIj40s8VmfkZrD1yFafm3FdKAdyDpB0OImuDbqedvxRjiOH\n1emriQ6LJvVoKp0adDqn++K+6UyuI5cACSCmVgxZ+VkUmkJa1GpxzrZjjCHhYAKtL2td6nc/+XAy\nDqeD1peXbfxxenY6v2b8SveI7j49pfN2zfOkwpfWsOctLSuNnVk76dqga7Esk6V7lhJRLYKmoU2L\nLZeRm0HiwUQ6N+js0+A65LshnoyWuQPmeq7RMnIzSDiYQJcGXUpsGC6LXw78wn0L7uOGRjfwaufS\nx8geyDlAwsEE2oe3p3ZwbYbOHerJAuka0ZX92ftJyUzh5U4vUye4DsGBwads3D+dvMI8lu5ZisPl\nICggiC4Rvu8xuyCbNQfW0KJWC3Ye3cl19a87xdrOvRxHDsv3LadPoz7nv2dORGKBH4ATdlEDYD/W\nOLl74Y+lWV7IYM7pcvJ73u96UvJzW49s5amfnuL5Ds+X+UCrlFLqpBOOE9w9726OFRzj33/5t08v\ngFtmXiahlUMvwN75L2MMmfmZJd79Tl2aDuQcwGmchIeEn/OG1NNx97C7b4B2rh0+cZjQyqHF7nZ9\nKu47bYPV4+peT90qdS+6hrXzSUT+vDFzXhtN42TPXAvgU07eAOUHIOp0N0C50MGcUkoppZRSl4Lt\nmdt5b8N73Blz50WTTr4vex//Xf9fYsJiypwKXR5d8GDOfj0GuA8oBP5hjJl3isUBDeaUUkoppZRS\nl7YzCebO2Y+GG2MaFnn9b+Df52r9SimllFJKKaVO+nOTc5VSSimllFJKnRMazCmllFJKKaWUH9Jg\nTimllFJKKaX8kAZzSimllFJKKeWHNJhTSimllFJKKT+kwZxSSimllFJK+SEN5pRSSimllFLKD52z\nHw0/F0TkMLD7Qu+Hn6sNZFzonVDnjNZn+aL1Wb5ofZYvWp/li9Zn+XKp1ecVxpg6ZZnxogrm1NkT\nkYSy/mK8uvhpfZYvWp/li9Zn+aL1Wb5ofZYvWp+l0zRLpZRSSimllPJDGswppZRSSimllB/SYK78\nefdC74A6p7Q+yxetz/JF67N80fosX7Q+yxetz1LomDmllFJKKaWU8kPaM6eUUkoppZRSfkiDOaWU\nUkoppZTyQxrMlRMi0ltEtonIDhF55kLvjzpJRKaKyCER2ehVFiYii0Rku/031Gvas3Y9bhORXl7l\nrURkgz3tDRERu7ySiHxhl68RkYZ/5vu71IhIhIj8KCKbRWSTiDxql2ud+iERqSwia0Uk2a7PF+xy\nrU8/JiIVRGS9iHxnv9b69FMikmbXQ5KIJNhlWp9+SkRqisgsEdkqIltEpIPW587aLPsAAAlRSURB\nVNnRYK4cEJEKwGSgD9AcGCIizS/sXikvHwC9i5Q9A/xgjIkCfrBfY9fbYKCFvcxbdv0CTAEeBKLs\nh3ud9wOZxpimwATg1fP2ThRAIfCEMaY50B4Yadeb1ql/yge6G2NaAnFAbxFpj9anv3sU2OL1WuvT\nv3UzxsR5/c6Y1qf/mgTMN8ZEAy2xvqdan2dBg7nyoS2wwxiTaowpAD4H+l/gfVI2Y8wy4EiR4v7A\nh/bzD4Gbvco/N8bkG2N2ATuAtiISDlQ3xqw21l2LPiqyjHtds4B4dwuVOveMMenGmHX28+NYJ6L6\naJ36JWPJtl8G2Q+D1qffEpEGwI3Ae17FWp/li9anHxKRGkBn4H0AY0yBMeYoWp9nRYO58qE+sMfr\n9V67TF28LjPGpNvPDwCX2c9Lq8v69vOi5T7LGGMKgSyg1vnZbeXNTt+4BliD1qnfslPykoBDwCJj\njNanf5sIjAJcXmVan/7LAItFJFFEhttlWp/+qRFwGJhmp0G/JyIhaH2eFQ3mlLrA7FYl/Y0QPyMi\nVYHZwD+MMce8p2md+hdjjNMYEwc0wGr1varIdK1PPyEifYFDxpjE0ubR+vQ7f7G/n32w0to7e0/U\n+vQrgcC1wBRjzDVADnZKpZvW55nTYK582AdEeL1uYJepi9dBO00A++8hu7y0utxnPy9a7rOMiAQC\nNYDfz9ueK0QkCCuQm26M+dIu1jr1c3a6z49YYy+0Pv3TdcBNIpKGNeSgu4h8gtan3zLG7LP/HgK+\nwhpaovXpn/YCe+3sB7DSIK9F6/OsaDBXPvwCRIlIIxGpiDVY9JsLvE/q1L4BhtnPhwFzvMoH23dj\naoQ1qHetnX5wTETa27nfdxdZxr2uQcASu2VLnQf2//99YIsxZrzXJK1TPyQidUSkpv08GOgBbEXr\n0y8ZY541xjQwxjTEOhcuMcbcidanXxKREBGp5n4O9AQ2ovXpl4wxB4A9InKlXRQPbEbr8+wYY/RR\nDh7ADUAKsBMYc6H3Rx8+dfMZkA44sFql7sfK3/4B2A4sBsK85h9j1+M2oI9XeWusk9hO4E1A7PLK\nwEysgcFrgcYX+j2X5wfwF6wUkF+BJPtxg9apfz6Aq4H1dn1uBJ6zy7U+/fwBdAW+0/r03wfQGEi2\nH5vc1zdan/77wLprcIJ9zP0aCNX6PLuH+40rpZRSSimllPIjmmaplFJKKaWUUn5IgzmllFJKKaWU\n8kMazCmllFJKKaWUH9JgTimllFJKKaX8kAZzSimllFJKqQtKRG4VkU0i4hKR1qeZt4KIrBeR77zK\nWorIKhHZICLfikj1IstEiki2iDxpv64iIt+LyFZ7u694zTtBRJLsR4qIHPWa5vSadtqfAivtfYlI\nDxFJtPc3UUS6l+0/5UuDOaWUUhc1EanldeI8ICL7vF6vPI/bbSgid5yv9Sul1KVKRLqKyAdFijcC\ntwDLyrCKR4EtRcreA54xxsRi/cD8U0WmjwfmFSl73RgTDVwDXCcifQCMMY8ZY+KMMXHAf4EvvZbJ\ndU8zxtxUhn0t7X1lAP3s/R0GfFyGdRWjwZxSSqmLmjHmd6+T6tvABK8TacfzuOmGgAZzSin1JzDG\nbDHGbDvdfCLSALgRK3jz1oyTAdMiYKDXMjcDu7B+r9C9vRPGmB/t5wXAOqBBCZscgvWbwafbr1Yi\n8pPdy7ZARMJP9b6MMeuNMfvtl5uAYBGpdLrtFKXBnFJKKb8lItn23672SXSOiKSKyCsiMlRE1top\nLE3s+eqIyGwR+cV+XGeXd/Hq7VsvItWAV4BOdtljdk/dchFZZz86nuG2PxCRt0UkwU7b6Xth/mtK\nKeXXJgKjAFeR8k1Af/v5rUAEgIhUBZ4GXihthSJSE+iH9ePl3uVXAI2AJV7Fle1zwGo7SEREgrB6\n8AYZY1oBU4F/n8F7GgisM8bkn8EyAASe6QJKKaXURaolEAMcAVKB94wxbUXkUeAR4B/AJKyevZ9F\nJBJYYC/zJDDSGLPCPvHnAc8ATxpj+oI1vgLoYYzJE5EorJba1mewbbB6+9oCTYAfRaSpMSbv/P1L\nlFLq4iEia4BKQFUgTESS7ElPG2MWlGH5vsAhY0yiiHQtMvk+4A0RGQt8AxTY5f/EOu5ni0hJ6wzE\nOp6/YYxJLTJ5MDDLGOP0KrvCGLNPRBoDS0RkAxAMXAUssrdRAUg/3fuxt98CeBXoWZb5i9JgTiml\nVHnxizEmHUBEdgIL7fINQDf7+fVAc68TenU7eFsBjBeR6cCXxpi9JZz0g4A3RSQOcGKl9JzJtgFm\nGGNcwHYRSQWigSSUUuoSYIxpB1ZGA3CPMeaeM1zFdcBNInIDUBnrGP6JMeZOY8xW7IBIRJphpWIC\ntAMGich/gJqAS0TyjDFv2tPfBbYbYyaWsL3BwMgi72Gf/TdVRJZijbfbBmwyxnQ4kzdjp4x+Bdxt\njNl5Jsu6aZqlUkqp8sI7PcXl9drFycbLAKC915i7+saYbGPMK8ADWK2rK0QkuoT1PwYcxOqFaw1U\nPMNtA5gi6yz6WimlVCmMMc8aYxoYYxpiBVpLjDF3AohIXftvAPD/sMZYY4zpZIxpaC8zEfg/dyAn\nIi8BNTiZPeFhnwdCgVVeZaHucW0iUhsruNyMFczVEZEO9rQgu8etVHZq5/dYN21Z8cf+IxrMKaWU\nurQsxEp7BMDuZUNEmhhjNhhjXgV+weoxOw5U81q2BpBu96zdhZVGc6ZuFZEAexxdY6wLAKWUuuSJ\nyAAR2Qt0AL4XkQV2eT0RmVuGVQwRkRRgK7AfmHaa7TUAxgDNgXX2+OgHvGYZDHxujPFudIsBEkQk\nGfgReMUYs9m+gcog4FV7WhLgHldd4vsC/gY0BZ7zGrNdtwzv04emWSqllLqU/B2YLCK/Yp0DlwEP\nA/8QkW5YPWmbsG5f7QKc9on5A+AtYLaI3A3MB3L+wPZ/A9YC1YGHdbycUupSZIxZCiwtUvYVVsph\n0Xn3Azecbh3GmElY46JPtd1/ej3fCxQfRFfCvF5lK4HYUuZPAjqXUF7a+3oJeOlU+1sW4htsKqWU\nUup8EOs3lb4zxsy60PuilFKqfNA0S6WUUkoppZTyQ9ozp5RSSimllFJ+SHvmlFJKKaWUUsoPaTCn\nlFJKKaWUUn5IgzmllFJKKaWU8kMazCmllFJKKaWUH9JgTimllFJKKaX80P8H4PmuVaVkPv4AAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f47cb873a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot the Sensor Values \n",
    "data.plot(x='Timestamp',y=['Ax','Ay','Az'],title=\"Acceleromter Training Raw Data\",figsize=(15.0, 4.0))\n",
    "data.plot(x='Timestamp',y=['Gx','Gy','Gz'],title=\"Gyroscope Training Raw Data\",figsize=(15.0, 4.0))\n",
    "data.plot(x='Timestamp',y=['MFx','MFy','MFz'],title=\"Magnetometer Training Raw Data\",figsize=(15.0, 4.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$\\epsilon  = Y_{Earth} - R_{t}.Y_{Device}$\n",
    "\n",
    "The Gauss-Newton method executes following iteration:\n",
    "\n",
    "$ q_t = q_{t-1} - (J_{t}^T.J_{t})^{-1}.J_{t}^T.\\epsilon$\n",
    "\n",
    "To represent the $q_{t}\\;at\\;t=0$ we have $Q_{observation} = [0.5,0.5,0.5,0.5]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## Initial Observation for Quaternion. \n",
    "Q_observation = np.matrix([[0.2], [-0.2] , [-0.5], [-0.15]])\n",
    "\n",
    "RowNumber = 1125\n",
    "## Call the GN Algorithm\n",
    "testObj = GaussNewtonOptimization(Q1=float(Q_observation[0]),\n",
    "                                                     Q2=float(Q_observation[1]),\n",
    "                                                     Q3=float(Q_observation[2]),\n",
    "                                                     Q4=float(Q_observation[3]),\n",
    "                                                     Ax=data['Ax'][RowNumber],Ay=data['Ay'][RowNumber],Az=data['Az'][RowNumber],\n",
    "                                                     Mx=data['MFx'][RowNumber],My=data['MFy'][RowNumber],Mz=data['MFz'][RowNumber])\n",
    "\n",
    "testObj = GaussNewtonOptimization(Q1=float(Q_observation[0]),\n",
    "                                                     Q2=float(Q_observation[1]),\n",
    "                                                     Q3=float(Q_observation[2]),\n",
    "                                                     Q4=float(Q_observation[3]),\n",
    "                                                     Ax=data['Ax'][RowNumber],Ay=data['Ay'][RowNumber],Az=data['Az'][RowNumber],\n",
    "                                                     Mx=data['MFx'][RowNumber],My=data['MFy'][RowNumber],Mz=data['MFz'][RowNumber])\n",
    "\n",
    "\n",
    "GN_output = testObj.Gaussnewton()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "q0 = list() ; q1 = list() ; q2 = list(); q3 = list()\n",
    "\n",
    "for i in range(len(GN_output)):\n",
    "    q0.append(float(GN_output[i][0]))\n",
    "    q1.append(float(GN_output[i][1]))\n",
    "    q2.append(float(GN_output[i][2]))\n",
    "    q3.append(float(GN_output[i][3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "GN_Q_0 = pd.DataFrame(\n",
    "    {'q0': q0,\n",
    "     'q1': q1,\n",
    "     'q2': q2,\n",
    "     'q3': q3\n",
    "    })\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "GN_Q_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f47cb8b4198>"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7wLKEb5w/n8uPnc5PH17Nt+58CbMzN7MpdMPS34ctjInaPQvCicF5P4CedfDQt/dsX0op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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f47cbc29550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outgraph = GN_Q_0.plot(x=GN_Q_0.index,y=['q0','q1','q2','q3'],title=\"Gauss Newton Quaternion Output\",\n",
    "            figsize=(15.0, 4.0)\n",
    "            ,legend=True)\n",
    "outgraph.set_xlabel(\"iteration number\")\n",
    "outgraph.set_ylabel(\"Quaternion value\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#np.arctan2(2*((GN_Q_0[\"q0\"]*GN_Q_0[\"q1\"])+(GN_Q_0[\"q2\"]*GN_Q_0[\"q3\"])), 1-2*(GN_Q_0[\"q1\"]*GN_Q_0[\"q1\"]+GN_Q_0[\"q2\"]*GN_Q_0[\"q2\"]) )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/omkar/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:3: RuntimeWarning: invalid value encountered in arcsin\n",
      "  app.launch_new_instance()\n"
     ]
    }
   ],
   "source": [
    "GN_Q_0[\"phi\"] = np.arctan2(2*((GN_Q_0[\"q0\"]*GN_Q_0[\"q1\"])+(GN_Q_0[\"q2\"]*GN_Q_0[\"q3\"])), 1-2*(GN_Q_0[\"q1\"]*GN_Q_0[\"q1\"]+GN_Q_0[\"q2\"]*GN_Q_0[\"q2\"]) )\n",
    "\n",
    "GN_Q_0[\"theta\"] = np.arcsin(2*((GN_Q_0[\"q0\"]*GN_Q_0[\"q2\"])-(GN_Q_0[\"q3\"]*GN_Q_0[\"q1\"])))\n",
    "\n",
    "GN_Q_0[\"psi\"] = np.arctan2(2*((GN_Q_0[\"q0\"]*GN_Q_0[\"q3\"])+(GN_Q_0[\"q1\"]*GN_Q_0[\"q2\"])), 1-2*(GN_Q_0[\"q2\"]*GN_Q_0[\"q2\"]+GN_Q_0[\"q3\"]*GN_Q_0[\"q3\"]) )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>q0</th>\n",
       "      <th>q1</th>\n",
       "      <th>q2</th>\n",
       "      <th>q3</th>\n",
       "      <th>phi</th>\n",
       "      <th>theta</th>\n",
       "      <th>psi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.567376</td>\n",
       "      <td>-0.567376</td>\n",
       "      <td>-1.418440</td>\n",
       "      <td>-0.425532</td>\n",
       "      <td>171.267952</td>\n",
       "      <td>NaN</td>\n",
       "      <td>161.595499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.371515</td>\n",
       "      <td>-0.027456</td>\n",
       "      <td>-1.081676</td>\n",
       "      <td>-0.518956</td>\n",
       "      <td>140.591892</td>\n",
       "      <td>-56.327058</td>\n",
       "      <td>-170.149761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.205256</td>\n",
       "      <td>0.384100</td>\n",
       "      <td>-0.707658</td>\n",
       "      <td>-0.787731</td>\n",
       "      <td>103.120926</td>\n",
       "      <td>18.338696</td>\n",
       "      <td>-145.095488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000739</td>\n",
       "      <td>0.367716</td>\n",
       "      <td>-0.570936</td>\n",
       "      <td>-0.793918</td>\n",
       "      <td>85.108255</td>\n",
       "      <td>35.663881</td>\n",
       "      <td>-155.230949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.003721</td>\n",
       "      <td>0.096710</td>\n",
       "      <td>-0.192237</td>\n",
       "      <td>0.107802</td>\n",
       "      <td>-2.660668</td>\n",
       "      <td>-1.112793</td>\n",
       "      <td>-2.409143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.007915</td>\n",
       "      <td>0.094052</td>\n",
       "      <td>-0.140281</td>\n",
       "      <td>-0.128148</td>\n",
       "      <td>2.093212</td>\n",
       "      <td>1.508527</td>\n",
       "      <td>-1.503924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.001462</td>\n",
       "      <td>0.024971</td>\n",
       "      <td>-0.046875</td>\n",
       "      <td>0.048702</td>\n",
       "      <td>-0.258875</td>\n",
       "      <td>-0.147218</td>\n",
       "      <td>-0.127133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.008194</td>\n",
       "      <td>0.047188</td>\n",
       "      <td>-0.072138</td>\n",
       "      <td>-0.019492</td>\n",
       "      <td>0.118585</td>\n",
       "      <td>0.173134</td>\n",
       "      <td>-0.375968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.003888</td>\n",
       "      <td>0.049280</td>\n",
       "      <td>-0.082491</td>\n",
       "      <td>0.071095</td>\n",
       "      <td>-0.662290</td>\n",
       "      <td>-0.438235</td>\n",
       "      <td>-0.444688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-0.012453</td>\n",
       "      <td>0.051874</td>\n",
       "      <td>-0.077722</td>\n",
       "      <td>-0.050670</td>\n",
       "      <td>0.383954</td>\n",
       "      <td>0.412109</td>\n",
       "      <td>-0.396519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.002679</td>\n",
       "      <td>0.022853</td>\n",
       "      <td>-0.034344</td>\n",
       "      <td>0.041980</td>\n",
       "      <td>-0.158734</td>\n",
       "      <td>-0.120478</td>\n",
       "      <td>-0.077506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-0.011089</td>\n",
       "      <td>0.034966</td>\n",
       "      <td>-0.056275</td>\n",
       "      <td>-0.013948</td>\n",
       "      <td>0.045916</td>\n",
       "      <td>0.127397</td>\n",
       "      <td>-0.209167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.004615</td>\n",
       "      <td>0.033597</td>\n",
       "      <td>-0.045056</td>\n",
       "      <td>0.054521</td>\n",
       "      <td>-0.265402</td>\n",
       "      <td>-0.233726</td>\n",
       "      <td>-0.146090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-0.015904</td>\n",
       "      <td>0.039754</td>\n",
       "      <td>-0.063976</td>\n",
       "      <td>-0.023299</td>\n",
       "      <td>0.099488</td>\n",
       "      <td>0.222730</td>\n",
       "      <td>-0.251312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.004503</td>\n",
       "      <td>0.030836</td>\n",
       "      <td>-0.036450</td>\n",
       "      <td>0.051161</td>\n",
       "      <td>-0.198685</td>\n",
       "      <td>-0.199590</td>\n",
       "      <td>-0.103212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-0.017429</td>\n",
       "      <td>0.035969</td>\n",
       "      <td>-0.060932</td>\n",
       "      <td>-0.016254</td>\n",
       "      <td>0.042072</td>\n",
       "      <td>0.188690</td>\n",
       "      <td>-0.220434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.005133</td>\n",
       "      <td>0.034261</td>\n",
       "      <td>-0.036006</td>\n",
       "      <td>0.053995</td>\n",
       "      <td>-0.203639</td>\n",
       "      <td>-0.233166</td>\n",
       "      <td>-0.110536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-0.020086</td>\n",
       "      <td>0.035028</td>\n",
       "      <td>-0.060976</td>\n",
       "      <td>-0.016852</td>\n",
       "      <td>0.037496</td>\n",
       "      <td>0.207992</td>\n",
       "      <td>-0.207624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.005206</td>\n",
       "      <td>0.035187</td>\n",
       "      <td>-0.033201</td>\n",
       "      <td>0.052517</td>\n",
       "      <td>-0.179652</td>\n",
       "      <td>-0.231565</td>\n",
       "      <td>-0.103336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-0.020881</td>\n",
       "      <td>0.031548</td>\n",
       "      <td>-0.056348</td>\n",
       "      <td>-0.016550</td>\n",
       "      <td>0.031638</td>\n",
       "      <td>0.194660</td>\n",
       "      <td>-0.165245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.004883</td>\n",
       "      <td>0.033852</td>\n",
       "      <td>-0.029175</td>\n",
       "      <td>0.047314</td>\n",
       "      <td>-0.139796</td>\n",
       "      <td>-0.199863</td>\n",
       "      <td>-0.087241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>-0.019761</td>\n",
       "      <td>0.026427</td>\n",
       "      <td>-0.048006</td>\n",
       "      <td>-0.015876</td>\n",
       "      <td>0.027658</td>\n",
       "      <td>0.156786</td>\n",
       "      <td>-0.109985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.004285</td>\n",
       "      <td>0.030255</td>\n",
       "      <td>-0.024413</td>\n",
       "      <td>0.039031</td>\n",
       "      <td>-0.094624</td>\n",
       "      <td>-0.147309</td>\n",
       "      <td>-0.065757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-0.016910</td>\n",
       "      <td>0.020444</td>\n",
       "      <td>-0.037230</td>\n",
       "      <td>-0.014617</td>\n",
       "      <td>0.022824</td>\n",
       "      <td>0.106387</td>\n",
       "      <td>-0.059086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.003561</td>\n",
       "      <td>0.024935</td>\n",
       "      <td>-0.019451</td>\n",
       "      <td>0.029128</td>\n",
       "      <td>-0.054859</td>\n",
       "      <td>-0.091165</td>\n",
       "      <td>-0.043799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-0.012970</td>\n",
       "      <td>0.014505</td>\n",
       "      <td>-0.025912</td>\n",
       "      <td>-0.012657</td>\n",
       "      <td>0.016053</td>\n",
       "      <td>0.059550</td>\n",
       "      <td>-0.024298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.002837</td>\n",
       "      <td>0.018837</td>\n",
       "      <td>-0.014758</td>\n",
       "      <td>0.019382</td>\n",
       "      <td>-0.026685</td>\n",
       "      <td>-0.046637</td>\n",
       "      <td>-0.025585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>-0.008826</td>\n",
       "      <td>0.009373</td>\n",
       "      <td>-0.015912</td>\n",
       "      <td>-0.010122</td>\n",
       "      <td>0.008982</td>\n",
       "      <td>0.026965</td>\n",
       "      <td>-0.006858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.002195</td>\n",
       "      <td>0.013019</td>\n",
       "      <td>-0.010692</td>\n",
       "      <td>0.011266</td>\n",
       "      <td>-0.010535</td>\n",
       "      <td>-0.019497</td>\n",
       "      <td>-0.013124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>-0.005309</td>\n",
       "      <td>0.005520</td>\n",
       "      <td>-0.008497</td>\n",
       "      <td>-0.007416</td>\n",
       "      <td>0.003864</td>\n",
       "      <td>0.009860</td>\n",
       "      <td>-0.000864</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          q0        q1        q2        q3         phi      theta         psi\n",
       "0   0.567376 -0.567376 -1.418440 -0.425532  171.267952        NaN  161.595499\n",
       "1   0.371515 -0.027456 -1.081676 -0.518956  140.591892 -56.327058 -170.149761\n",
       "2   0.205256  0.384100 -0.707658 -0.787731  103.120926  18.338696 -145.095488\n",
       "3   0.000739  0.367716 -0.570936 -0.793918   85.108255  35.663881 -155.230949\n",
       "4  -0.003721  0.096710 -0.192237  0.107802   -2.660668  -1.112793   -2.409143\n",
       "5  -0.007915  0.094052 -0.140281 -0.128148    2.093212   1.508527   -1.503924\n",
       "6   0.001462  0.024971 -0.046875  0.048702   -0.258875  -0.147218   -0.127133\n",
       "7  -0.008194  0.047188 -0.072138 -0.019492    0.118585   0.173134   -0.375968\n",
       "8   0.003888  0.049280 -0.082491  0.071095   -0.662290  -0.438235   -0.444688\n",
       "9  -0.012453  0.051874 -0.077722 -0.050670    0.383954   0.412109   -0.396519\n",
       "10  0.002679  0.022853 -0.034344  0.041980   -0.158734  -0.120478   -0.077506\n",
       "11 -0.011089  0.034966 -0.056275 -0.013948    0.045916   0.127397   -0.209167\n",
       "12  0.004615  0.033597 -0.045056  0.054521   -0.265402  -0.233726   -0.146090\n",
       "13 -0.015904  0.039754 -0.063976 -0.023299    0.099488   0.222730   -0.251312\n",
       "14  0.004503  0.030836 -0.036450  0.051161   -0.198685  -0.199590   -0.103212\n",
       "15 -0.017429  0.035969 -0.060932 -0.016254    0.042072   0.188690   -0.220434\n",
       "16  0.005133  0.034261 -0.036006  0.053995   -0.203639  -0.233166   -0.110536\n",
       "17 -0.020086  0.035028 -0.060976 -0.016852    0.037496   0.207992   -0.207624\n",
       "18  0.005206  0.035187 -0.033201  0.052517   -0.179652  -0.231565   -0.103336\n",
       "19 -0.020881  0.031548 -0.056348 -0.016550    0.031638   0.194660   -0.165245\n",
       "20  0.004883  0.033852 -0.029175  0.047314   -0.139796  -0.199863   -0.087241\n",
       "21 -0.019761  0.026427 -0.048006 -0.015876    0.027658   0.156786   -0.109985\n",
       "22  0.004285  0.030255 -0.024413  0.039031   -0.094624  -0.147309   -0.065757\n",
       "23 -0.016910  0.020444 -0.037230 -0.014617    0.022824   0.106387   -0.059086\n",
       "24  0.003561  0.024935 -0.019451  0.029128   -0.054859  -0.091165   -0.043799\n",
       "25 -0.012970  0.014505 -0.025912 -0.012657    0.016053   0.059550   -0.024298\n",
       "26  0.002837  0.018837 -0.014758  0.019382   -0.026685  -0.046637   -0.025585\n",
       "27 -0.008826  0.009373 -0.015912 -0.010122    0.008982   0.026965   -0.006858\n",
       "28  0.002195  0.013019 -0.010692  0.011266   -0.010535  -0.019497   -0.013124\n",
       "29 -0.005309  0.005520 -0.008497 -0.007416    0.003864   0.009860   -0.000864"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GN_Q_0.head(30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f47cb89d9e8>"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eqH0Iz765inX1TYUOR0RERERESlBBkz4zu9XMVprZ/M7sn4glinLKhkzTJg6l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\nGWB6mNYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f47cbc0ef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outgraph2 = GN_Q_0.plot(x=GN_Q_0.index,y=['phi','theta','psi'],title=\"Gauss Newton Output for Roll, Pitch, Yaw in Radians\",\n",
    "            figsize=(15.0, 4.0),legend=True)\n",
    "outgraph2.set_xlabel(\"iteration number\")\n",
    "outgraph2.set_ylabel(\"phi, theta, psi\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "GN_Q_0[\"phi\"] = GN_Q_0[\"phi\"]*57.2958\n",
    "GN_Q_0[\"theta\"] = GN_Q_0[\"theta\"]*57.2958\n",
    "GN_Q_0[\"psi\"] = GN_Q_0[\"psi\"]*57.2958"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f47cb691208>"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tg3zlIxN4YMkaPnzlAh6rWFvosEREREREpI9oM1E0s73N7EZgvrtvNbOp4aQz\nPUo8Fgco+C0yshUrjvKNj03koa9+kGHlpfzvgxWFDklERERERPqIbIae3gw8THBLCoBXCYaf9ig9\nLVFM23+vAXzmfeNYsW4bK9ZqRlQREREREcm/bBLFoe5+N5ACcPcGIOvbUnQXg0oHEbUoVTXdf+hp\nU8dOG44ZPLT0vUKHIiIiIiIifUA2ieJ2M0uwa9bTw4HuN3VoGyIWYUhsSI+rKALsPTDG7H2G8OCS\nHjfZrIiIiIiI9EDZJIrfAO4H9jOzfwK3AF/Oa1R5Eo/Fe8RkNs05btoIKt7bymvrtxU6FBERERER\n6eVaTRTNLALEgKOA9wP/ARzg7i93QWw5l4gluvXtMVpz3PThAPxdw09FRERERCTPWk0U3T0FXOvu\nDe6+zN2Xunt9F8WWc/GynltRHDGojIPHDuaBlzX8VERERERE8iuboaePmtknzMzyHk2exWPxHnmN\nYtrx00fwypotrNqwvdChiIiIiIhIL5ZNovgfwD1AnZltMbOtZrYlz3HlRSKWoKahhh31OwodSocc\nN30EoNlPRUREREQkv9pMFN293N0j7l7i7gPD5YFdEVyu9dR7KaaNGlzGgWMGa/ZTERERERHJqzYT\nRTM7uJnHfmZW1BUB5lKiLAH03EQR4Phpw1nyzmberu6ZVVEREREREen+shl6eh3wL+CG8PEvgqGo\nlWb28TzGlnM9vaIIwXWKAA8tVVVRRERERETyI5tE8V3gIHef5e6zgJnA68DHgMvzGVyuJWJBRbGq\npmfOfAowJt6P6aMG8cASXacoIiIiIiL5kU2iONHdl6UX3P0VYLK7v56/sPJjSGwI0LMrihBUFV96\nexOrN2r4qYiIiIiI5F42ieIyM/u1mR0VPq4DXjGzUqBH3VMxVhSjf3H/Hp8oHjdtOAB/1+ynIiIi\nIiKSB9kkiucAK4GvhY/Xw3X1wNH5CixfErFEjx56CjBuaH+mjhio2U9FRERERCQv2py51N1rwiri\n39y9ssnmbfkJK3/isXiPrygCnDBjBFc8XMmazTWMGFRW6HBERERERKQXyeb2GCcBLwJ/D5dnmtn9\n+Q7MzFaZ2RIze9HMFoXr4mb2DzNbEf4c0t5247E4VbU9u6IIGn4qIiIiIiL5k83Q0x8AhwKbANz9\nRWB8PoPKcLS7z3T32eHyJcCj7j4BeDRcbpdEWaJXVBT3HTaAycPLNfxURERERERyLptEsd7dNzdZ\n5/kIJgucqfn4AAAgAElEQVQnA38In/8BOKW9DcRjcTbWbiSZSuY0sEI4fvoIFr25kbVbagsdioiI\niIiI9CLZznr6aSBqZhPM7GrgmTzHBUEy+oiZLTaz88J1e7t7uoT2HrB3cwea2XlmtsjMFq1fv363\nbfFYHMfZVLcpb4F3leOnD8cdHl6m4aciIiIiIpI72SSKXwYOAOqAO4AtBLOf5tuR7j4TOA64yMw+\nmLnR3Z0WKpvufr27z3b32cOGDdttW6IsAdArrlPcf69yJuw1gAde1vBTERERERHJnTYTRXff4e7f\nc/dDwuTre+6e97GO7v5O+HMdcC/BdZJrzWwEQPhzXXvbjcfiAL3iOkUIhp8uXFXN+q11hQ5FRERE\nRER6iRYTRTP7q5nd39Ijn0GZWX8zK08/Bz4OLAXuBz4b7vZZ4L72tp2IBRXF6prekyhq+KmIiIiI\niORSa/dRvDL8eRowHLgtXP4UsDafQRFce3ivmUEQ4+3u/nczew6428zOBd4Ezmhvw+mhp72lojhx\n7wHsO6w/Dy5Zw7zD9yl0OCIiIiIi0gu0mCi6+xMAZvazjNtTAPw1fV/DfHH314EDm1lfBXykM22X\nl5RTZEW94hpFADPjhOkjuPbxlVRtqyMxoLTQIYmIiIiISA+XzWQ2/c1s3/SCmY0H+ucvpPyKWIQh\nsSG9pqIIcNy0EaQc/u+VfBd6RURERESkL8gmUfw6sMDMFpjZE8DjwFfzG1Z+xWPxXnONIsCUEeWM\nS/TjwSWa/VRERERERDqvtWsUAQivDZwATA5XVbh7j55iM1GW6DlDT197DB7+HgyfAaf+BoLrNndj\nZhw/fQS/ffJ1Nm7fyZD+JQUIVEREREREeotsKoq4e527vxQ+enSSCGFFsbsPPd30Ntx1Ntx6Kmxb\nCy/fCc/8qsXdj58+gmTK+YeGn4qIiIiISCdllSj2Nt06UWyog6d+BtceCiv+AR/+Pnz9FZh6Cjxy\nKbz+RLOHHTByIGPiZTyg4aciIiIiItJJfTJRTJQlqGmoYUf9jkKHsruVj8B174NHfwT7fwS+tBA+\neDEUx+Dka2DoRJj/Odi8eo9D08NP/7lyA5t31BcgeBERERER6S2yShTNbJSZvd/MPph+5DuwfIrH\n4gDd5zrFTW/DXfPgtk8Ey/P+BGfeBoPH7tqntDxY17AzGJJaX7tHM8dPG0FDyvnHcg0/FRERERGR\njmtzMhsz+ylwJvAKkAxXO/BkHuPKq3SiWF1bzZjyMYULpKEOnrkanrwyWP7If8P7vgRFLdwLceiE\nYEKbu+bCQ9+Gk3a/ZnHG6EGMGlzGg0vWcPqs0XkOXkREREREeqs2E0XgFGBSb5jEJi1RlgCgqqaA\nFcUVjwTJXvVrMOUkOObHMDiLpHXKHPjAN4PrGEfPhoM/07gpGH46nJufWcWW2noGxorz+AJERERE\nRKS3ymbo6etAr8o4ErEgUSzIhDab3oI758IfPxHc6mLen+HMW7NLEtOO/h7s92F44FvwzuLdNh03\nfQT1SedRDT8VEREREZEOyiZR3AG8aGa/NbNfpR/5DiyfhsSGAF2cKDbUwZNXwDWHBvdG/MgP4IJn\ngklr2isShU/cCAP2hrs+A9s3NG6aOXowIwbFeODl93IYvIiIiIiI9CXZDD29P3z0GqXRUsqLy7su\nUVzxj3CY6esw9WT4+GXtqyA2p188qETe+HGY//mgMhktIhIxjps2gtv+/SZba+sp1/BTERERERFp\npzYriu7+h+YeXRFcPsXL4l1zjeIzV8MfTweLwtn3whm3dD5JTBs5E+b8HN54Ah77f42rj58+nJ0N\nKR6rWJebfkREREREpE9psaJoZne7+xlmtoRgltPduPuMvEaWZ/FYPP8VxWQDPHstjPtAUPErKsl9\nHwfNhXcWwT9/AaMOhqknc/DYIew9sJQHl6zh5Jmjct+niIiIiIj0aq0NPf1q+HNOVwTS1eKxOG9u\neTO/nbz2KGxdA8ddnp8kMe3Yn8Cal+EvF8KwyUSGTeK4aSO4Y+FbbK9roH9pNiOMRUREREREAi0O\nPXX3NeHPN5t7dF2I+ZGIJfI/9PT5W6DfUJh4bH77KSoNhrQWl8Fd86BuK8dNG05dQ4rHKzX8VERE\nRERE2iebWU97pXhZnE11m2hINeSng23r4NW/w8xP5beamDZoFJz+e6h6Df5yIbP3GcLQAcHwUxER\nERERkfbou4liLI7jbKrblJ8OXroTUg1w0Gfy035zxn8APvYjWH4/0Wd/xXHThvN4xXp27MxTMiwi\nIiIiIr1Sn00UE7EEQH6Gn7rDC7fCmMNg2MTct9+a910EB5wGj/6Qs4a+Rk19kicq13dtDCIiIiIi\n0qO1mCia2d3hzyVm9nLGY4mZvdx1IeZHPBYHyM/Mp28vhA2vwkFn577ttpjBSVfD0ElMfebrHNBv\nMw9o+KmIiIiIiLRDaxXFzFlPT8x4pJcLwsyONbNKM1tpZpd0tJ14WR4TxRdugZIBcMCpuW87G6UD\n4MzbsGQ9vy39JU9XrKa2PlmYWEREREREpMdp8b4J6VlPgQ1AjbunzGwiMBl4qCuCa8rMosC1wMeA\n1cBzZna/u7/S3rbyNvS0bissvRemnRYkbIUydH849beMvvNTXJK6kSdePZRjDhjeribcnfVba3n9\nnbW8u/pNtmzaQEnZQPoPHEz/QXEGDxxMfEApif6lDCwrwszy9GJERERERKQrZXODvSeBD5jZEOD/\ngOeAM4G5+QysBYcCK939dQAzuxM4GWh3ojiwZCBFVpT7iuLSP0P9dji4Cyexacnk40kd+U3Oevpn\n3PnUDXDAfwXr3YOEdvt62LYW37aOrRveZdP6d9ixcQ2prWspqllP//pq4r6Zw21ns80n3dhGGVvp\nx7vej9pof3ZG+1NfXE6yZAB1pf2pL+tHQ6yMZFkMj8WguAg8hTmQciyVwj2FuRNJOZ5KYTiWTIE7\nFm4jlcJSjnkSsyiRaDGRomIi0WKiRSVEoyVEiouJRkuIFhdTVFRCcXEp0eISSopLiJYUU1wUo6S4\nBIsW48l6du6soa6mlvr6GnburKOhrob6nTU07KwjVV9HQ30tqfpakg07SdXX4ck6qK/DU/V4sh6P\nRElGIqQiUVKRKESKSGUseyQCkSgeDZ4Hj2iwLmJYJIKnHDx8rXjwWt2Dc4OH61PBsjuE+1h4DBhY\n0K5ZBCIRsKBfa3wewSyIwSwSrA/XWSSKp5JBDKlkcP6TDbvWeRJPJrFU8JxUKpikKZUK3ov0fhae\nAwtfZxhT5jIWhYgF58XC82DhecCC9j0V9hW818FnJAk4pJJEPIWnPwdhzOnz4aTbjjT2kRkH6ffD\nDLfobucKC86Ne6rxXBC+5qCf1K7XmkqGn8tk4/Ng31QQR9h3KuzDiTR5zUEswXnZFVv6HJkZnj63\njec9Gbzfvuu9sFQKSDXuE8mIL2jTSJFuO3wvwtebwhpjs8ZzEp6P9LkKv5vpz0Hw2Qz6c1LhZ3DX\na8dTRNKfSw/eMycSvMfpvsN+3AwIlgnXp2MFgnNlFnzECfr18GdjHOH3Y9fz9OfGg/PiKdw96AOC\nfgBv7Ncg+NZhRhAfu9bv2h7GkP7diYeLQb/uBN9RD14x4XODMLYmMtu1xv+EP233dbvFQOPvhPRy\n5rPG+DxjufFna5r5Bz7LjCV77t50Rfsa2K1/Ecmbjn43M+l72idkkyiau+8ws3OB69z9cjN7Md+B\ntWAU8HbG8mrgsKY7mdl5wHkAY8eObbYhMyMei+c+UXzhVhg2GUYfktt2Oyjy4e9R+eJTnLbmF6Su\nf4z6reuor1lPQ6qeOjN2mlFnRp1BDRGqrD/VkQFsKytn55D9SJWVY/3LKRowAEqL2Va3nS11W9lW\nt53tDTvYkaylJrWTWq+nlhpq2U6traUukvELZGf42Fyos5AjEaA0i/3Cv99FRERERHqqrBJFM3sf\nQQXx3HBdNH8hdZ67Xw9cDzB79uwW/9kkUZbIbaK4rgJWPwcfv6z7/EtLJMrqj/6M/3juM2ws3kBq\naATYO4sDt4YPoCZ8ACWREvoV96NfUT/6lQ2gX9FeDC4uo39R/13rM37GKMJ3pvDaerx2J+xMQjSC\nYXgk/Ff7SFBlsAhh9YOwAgEWCbYDeISg8pFK0dBQTzJZT0NDA8mGelLJBpLJBlKpBpINDSST9Xgy\nSSrVgIfrU6kkngqqZRYpwqJFQWUyWkKkqIiiohIiRcVEo8VEi0soKi6hqKiEouJiiotKKSkppiga\nJRK+txGLELEIUYsCkaCikExCMqh6eSqstiSDypAnw2pZKqjSecqxSFBtSZlhYZUnXWHBCKsx4Xos\nrMAF563xg51Kha8tuasK1LhuV9XHMyplnrnOLKiqRYLqEumHRbBoUHU0i2LRcJ/oruqlhe8lHlaD\nw4rfropcCk8FD2vcHlTjPDwXQYUMiKZfe1Bx9bACiUXDz0F0V6xmjRVKS8cKkEqS8l3Vv8Zzksqs\nfqWrdekKWUNY2Q6rT5EIRIoa+01ZOKw6PBeejildMYxEiESKsIjtKuakkkGlvLGf9HlPV2XT1dP0\n6w9iTVdPPVIUvhcGVhR+LqLhuoxKaCSMLb0+UgTBOxJUg913VSbZdb5TnsRS6Qpd2HfG+cFTjVVA\nixRlnPd0ddrC1x8l0li9Dd6LxvfDCCvmviuWsEoM4efE05XSdOV0V8XcU8ngtTVWytNVrqLG3wtG\npLEaHPyeiIbHBPEaFlZow/e3sa90ZTCMxzwsUIbnI71vupoffv+CPndVHI1dFdH0w8KKpYXxWrpS\niQffN5xdlciwXtnYH41VSMPDCp2HtdmMKQXMwhZ39bPb/3MsI86MdY32qCb4bs/33JxekWKPqQ2a\n/L8u0mS5vVXJtoqgKfc9+ygAD85+n4+hu8TRHWLoLnFkHUNnwsyiINmjzkUfiMNxjuSEdh+XTaL4\nNeC7wL3uvszM9gUeb3dPufEOMCZjeXS4rkPisXhur1F84VaIFMOBZ+WuzRwYsPdOqkqSjC05kn0G\n7sPw8gGMGFjO4H79KI2WNj5KoiWtPi+JllAcKS70yxERERERkTxrM1F09yeAJ8xsoJmVh9cHfiX/\noTXrOWCCmY0nSBDPAj7d0cbisThvbH4jN5E17ISX7oBJx0H/oblpM0dWbqoE4Pcn/5C9+u1V4GhE\nRERERKS7a+32GACY2WwzWwK8DCw1s5fMbFb+Q9uTuzcAXwIeBpYDd7v7so62l75GcY8L8Dvi1Ydg\nR1X3mMSmiYrqCuKxOMPKhhU6FBERERER6QGyGXp6E3Chuz8FYGZHAr8HZuQzsJa4+4PAg7loK1GW\noDZZy46GHfQv7t+5xp6/BQaOgv0+nIvQcqqiuoLJ8cm6fYWIiIiIiGSlzYoikEwniQDu/jTQkL+Q\nuk48FgeguqaTE9psXg0rH4WZnw4mfOhG6pP1rNy0ksnxyYUORUREREREeohsEsUnzOy3ZvYhMzvK\nzK4DFpjZwWZ2cL4DzKd0olhV28kJbV68HXA4aF7ng8qx1za/RkOqQYmiiIiIiIhkLZuhpweGP3/Q\nZP1BBBPkdr+xlllKlCWATiaKqVQw2+n4o2DIuNwElkMV1RUATIpPKnAkIiIiIiLSU2Qz6+nRXRFI\nITQOPe3MvRRXPQmb3oKPNM2ju4fK6krKisrYp3yfQociIiIiIiI9RDZDT3utnFyj+PytEBsMk+fk\nKKrcWl69nAlDJhDtZtdOioiIiIhI99WnE8WSaAnlJeUdH3q6oxqW/xVmnAHFsdwGlwPuTmV1JVPi\nUwodioiIiIiI9CB9OlEESMQSHR96uuQeSNbBQWfnNqgcWb1tNdvqt+n6RBERERERaZd2J4pmNtvM\nRuYjmEKIx+IdSxTdg2GnIw6EEQW5pWSbKqsrAVRRFBERERGRdulIRfHLwANmdleugymERFmCqpoO\nDD1d8yKsXdJtq4kQXJ8YsQj7D96/0KGIiIiIiEgPks3tMXbj7p8FMLPy3IfT9eKxOM/VPtf+A5+/\nFYpiMP2TuQ8qRyqrKxk/cDyxou53/aSIiIiIiHRfWSWKZjYEmAA0Zhzu/mS+gupK8VicTXWbaEg1\nUBTJMm+ur4El82HqyVA2OL8BdkJFdQWzh88udBgiIiIiItLDtJkZmdkXgK8Co4EXgcOBZ4EP5ze0\nrpGIJQDYVLeJoWVDszvolfuhbnO3Hna6sXYja3esZfKQyYUORUREREREephsrlH8KnAI8Ka7Hw0c\nBGzKa1RdKF4W3EuxXdcpvnArDBkP447MU1SdV1FdAcDkhBJFERERERFpn2wSxVp3rwUws1J3rwB6\nzf0W4rEwUcz2XopVr8Gqp+CgeWCWx8g6pzFRVEVRRERERETaKZuL8lab2WDgL8A/zGwj8GZ+w+o6\n6UQx61tkvHAbWARmfjqPUXVeRXUFw/sPZ3Cs+15DKSIiIiIi3VObiaK7nxo+vdTMHgcGAQ/lNaou\nlCgLrlHMauhpsgFevB32/xgM7N63kqyorlA1UUREREREOqTNoadmdmv6ubs/4e73AzflNaouVF5c\nTlGkKLuK4spHYNt7cPBn8h9YJ9Q01LBqyypdnygiIiIiIh2SzTWKB2QumFkUmJWfcLqemRGPxbNL\nFF+4FfrvBROPyX9gnbBi4wpSnlJFUUREREREOqTFRNHMvmtmW4EZZrbFzLaGy+uA+7oswi6QiCXa\nHnq6bR28+nc48CyIFndNYB2UnshmUrzXzDkkIiIiIiJdqMVE0d3/193LgSvcfaC7l4ePhLt/twtj\nzLt4WRYVxZfugFRDt753YlpldSXlxeWMGjCq0KGIiIiIiEgPlM3Q0++Z2Twz+y8AMxtjZofmKyAz\nu9TM3jGzF8PH8RnbvmtmK82s0sxyNv4zEUu0nii6w/O3wpjDYdjEXHWbNxXVFUyKT8K68e07RERE\nRESk+8omUbwWeB+Qvh/EtnBdPv3c3WeGjwcBzGwqcBbBNZPHAteF10t2Wnroqbs3v8Nb/4KqFXBw\n968mJlNJXt34KpPjuj5RREREREQ6JptE8TB3vwioBXD3jUBJXqNq3snAne5e5+5vACuBnFQ247E4\nO1M72V6/vfkdXrgVSgbA1FNy0V1evbnlTWqTtUoURURERESkw7JJFOvDyp0DmNkwIJXXqODLZvay\nmd1kZkPCdaOAtzP2WR2u24OZnWdmi8xs0fr169vsLF4WB2h++GntFlh2L0z7BJQOaN+rKID0RDZK\nFEVEREREpKOySRR/BdwL7GVmlwFPAz/uTKdm9oiZLW3mcTLwa2BfYCawBvhZe9t39+vdfba7zx42\nbFib+ydiCaCFRHHZn6F+R7e/d2JaRXUFxZFi9h20b6FDERERERGRHqqorR3c/Y9mthj4CGDAKe6+\nvDOduvtHs9nPzG4A/hYuvgOMydg8OlzXafFYUFFs9hYZz98Kw6bAqJ5x68iK6gr2H7w/xd38Fh4i\nIiIiItJ9ZVNRBFhBUFW8H9huZmPzFZCZjchYPBVYGj6/HzjLzErNbDwwAViYiz4bE8XaJoniuuXw\nzqJgEpseMIOou1O5sVLDTkVEREREpFParCia2ZeBHwBrgSRBVdGBGXmK6XIzmxn2sQr4DwB3X2Zm\ndwOvAA3ARe6ezEWH6URxj6Gn29fD3tNgxpm56Cbv1u1YR3VtNZPikwodioiIiIiI9GBtJorAV4FJ\n7t7MuMzcc/cW70Hh7pcBl+W6z+JoMQNLBu459HT8B+GCf+a6u7yp3FgJwJT4lAJHIiIiIiIiPVk2\nQ0/fBjbnO5BCi8fizU9m04MsrwouHZ04ZGKBIxERERERkZ6sxYqimX0jfPo6sMDMHgDq0tvd/ao8\nx9alekOiWLmxkrHlYxlQ0v1v4yEiIiIiIt1Xa0NPy8Ofb4WPkvAB4T0Ve5NEWYKVm1YWOoxOWV61\nnCkJDTsVEREREZHOaTFRdPcfApjZJ939nsxtZvbJfAfW1Xp6RXHrzq2s3raa0yacVuhQRERERESk\nh8vmGsXvZrmuR0vEEmyu20x9qr7QoXRIZXUwkY1mPBURERERkc5q7RrF44DjgVFm9quMTQMJbk/R\nqyTKEgBsrN3IXv32KnA07Zee8VT3UBQRERERkc5q7RrFd4FFwEnA4oz1W4Gv5zOoQsi8l2JPTBQr\nqiuIx+IMKxtW6FBERERERKSHa+0axZeAl8zsdnfvmeMx26ExUazpmdcpVlRXMDk+GTMrdCgiIiIi\nItLDtXmNYl9IEmHX0NOq2qoCR9J+9cl6Vm5aqWGnIiIiIiKSE9lMZtMnZA497Wle2/waDakGJYoi\nIiIiIpITShRDA4oHUBwp7pEVxYrqCkAT2YiIiIiISG60NplNs8zsx8Bm4Hfu3vOyqhaYGYmyRI+8\nRrGiuoKyojLGlo8tdCgiIiIiItILdKSiuJDg9hg/z3EsBRePxXtsRXHCkAlEI9FChyIiIiIiIr1A\nuyuK7v6XfATSHcRj8R53jaK7U1ldyQn7nlDoUEREREREpJdoMVE0s2+7++VmdjXgTbe7+1fyGlkB\nxGNxVm5aWegw2mX1ttVsq9/GpPikQociIiIiIiK9RGsVxeXhz0VdEUh3kChLUFVThbv3mPsRVlZX\nAjAlPqXAkYiIiIiISG/RYqLo7n8Nf/6h68IprEQsQX2qnm312ygvKS90OFlZXr2cqEXZf/D+hQ5F\nRERERER6iTavUTSzicC3gHGZ+7v7h/MXVmFk3kuxpySKldWVjB80nlhRrNChiIiIiIhIL5HNZDb3\nAL8Bfgck8xtOYSViCQCqaqrYZ+A+BY4mO8url3PI8EMKHYaIiIiIiPQi2SSKDe7+67xH0g3Ey3ZV\nFHuC6tpq1u1Yp+sTRUREREQkp1q8j6KZxc0sDvzVzC40sxHpdeH6DjOzT5rZMjNLmdnsJtu+a2Yr\nzazSzI7JWD/LzJaE235leZhtJnPoaU+QnshGM56KiIiIiEgutVZRXExwW4x0QnZxxjYH9u1Ev0uB\n04DfZq40s6nAWcABwEjgETOb6O5J4NfAF4F/Aw8CxwIPdSKGPQyJDQGCoac9QUV1BQCTh0wucCQi\nIiIiItKbtDbr6fh8deruy4HmbkFxMnCnu9cBb5jZSuBQM1sFDHT3f4XH3QKcQo4TxeJIMYNKB1FV\n23MSxeH9hzM4NrjQoYiIiIiISC+SzaynMeBC4EiCSuJTwG/cvTYP8YwC/pWxvDpcVx8+b7q+WWZ2\nHnAewNixY9sVQDwW7zFDTyuqK1RNFBERERGRnGvxGsUMtxAMBb0auCZ8fmtbB5nZI2a2tJnHyZ0L\nuW3ufr27z3b32cOGDWvXsYlYokckijUNNazasorJCSWKIiIiIiKSW9nMejrN3admLD9uZq+0dZC7\nf7QD8bwDjMlYHh2ueyd83nR9zsVjcV7d+Go+ms6pFRtXkPKUKooiIiIiIpJz2VQUnzezw9MLZnYY\nsChP8dwPnGVmpWY2HpgALHT3NcAWMzs8nO30M8B9+Qigpww9bZzIRhVFERERERHJsWwqirOAZ8zs\nrXB5LFBpZksAd/cZ7e3UzE4lGMo6DHjAzF5092PcfZmZ3Q28AjQAF4UznkJwneTNQBnBJDY5ncgm\nLV4WZ8vOLdQn6ymOFueji5yoqK6gvLickf1HFjoUERERERHpZbJJFI/Ndafufi9wbwvbLgMua2b9\nImBarmNpKhFLAMG9FPfuv3e+u+uwyupKJsUnNTdzrIiIiIiISKe0mSi6+5tdEUh30RMSxWQqyasb\nX+X0iacXOhQREREREemFsrlGsU+Jl8UBuvV1im9ueZPaZC2T47o+UUREREREck+JYhPpimJVbVWB\nI2lZ40Q2ShRFRERERCQPlCg2EY+FFcWa7ltRrKiuoDhSzL6D9y10KCIiIiIi0gspUWyif3F/SiIl\n3XroaUV1BfsP3p/iSPedlVVERERERHouJYpNmBmJskS3HXrq7lRUV2jYqYiIiIiI5I0SxWbEY/Fu\nmyiu27GOjXUblSiKiIiIiEjeKFFsRjwW77bXKFZurAQ0kY2IiIiIiOSPEsVmJMoS3fYaxeVVywGY\nOGRigSMREREREZHeSoliM+KxONW11bh7oUPZQ+XGSsaWj2XA/2/v3oP0qus7jr8/STC7BCrZDUQm\nIQY04SLKIghBwQvKLXXwgpU2anEcpFRsbJU6YJyRanF0pB0ztXTKKIqjtaMCygjh7gXoAEIMEk3C\nnTEoBhOQBCXk8u0fzwnuxs1lk2yeh837NbOz5/zO7bvJd5J8cn7nPC/ao92lSJIkSRqhDIqD6Onq\nYc36Naxcs7LdpfyZRcsXcWDPge0uQ5IkSdIIZlAcRKd+luLK51aydNVSDu45uN2lSJIkSRrBDIqD\n6O3uBei4N58uWdF6kY13FCVJkiQNJ4PiIHq7WkGx015os+GNp95RlCRJkjScDIqD6NSpp4uWL6Kn\nq4cJ3RPaXYokSZKkEcygOIjxXeOBDpx6+uQSDuo5iCTtLkWSJEnSCGZQHMSYUWPYa+xeHTX1dM26\nNTzw1AMc1HNQu0uRJEmSNMIZFDdhw2cpdooHf/8ga9evNShKkiRJGnYGxU3o7e5l+R87Z+rp4hWL\nAQyKkiRJkoadQXETdtQdxaeefYoFyxawdv3a7TrP4hWL6R7TzZQ9p2x3TZIkSZK0OWPacdEkfwVc\nABwMHFVVdzXjU4FFwJJm19ur6uxm2xHA14Bu4BrgI1VVw1VjT1fPdr/MZvGKxZxz4zks++Myerp6\nOGnqSczcfyaH7X3YkF9Is3jFYqaPn87oUaO3qyZJkiRJ2pJ23VFcCLwT+Mkg2x6sqr7m6+x+4/8F\nfBCY1nydPJwF9nb1svK5laxZt2abjr9l6S2cMe8MknDBMRdwxMQjuOL+K3jfvPdxyhWnMHf+XO5/\n8v6tOtf6Ws+SFUucdipJkiRpp2jLHcWqWgRs9V21JPsCf1FVtzfrXwfeDswbrhp7ulufpbj82eW8\nZB1Rk3kAAAsqSURBVNxLhnTsd+77DhfefiHTxk/jS8d/iYnjJnLa9NNY9dwqbv7VzVzz0DV8deFX\n+fK9X2ba+GnM3H8mp+x/CpP2mDTo+R5b9Rir1qwyKEqSJEnaKdoSFLdg/yQLgN8Dn6yqW4BJwNJ+\n+yxtxgaV5CzgLIApU7btmb6erlZQXPHsiq0OiutrPXPnz+XShZdy7KRjuegNFzFut3HPb9/jRXtw\n6stO5dSXncrv/vg7rn/keuY9PI+58+cyd/5c+vbuY+YBMznxpSfS2937/HFLVrRm4hoUJUmSJO0M\nwxYUk9wIDJaw5lTV9zdx2G+AKVW1vHkm8XtJXjHUa1fVJcAlAEceeeQ2PcfY29UKalv7QpvV61Yz\n59Y5XPfIdbx7+rs5/+jzGTNq07+8E7onMOvgWcw6eBZLVy7l2keu5eqHruazd3yWz9/5eWbsO4OZ\nB8zk+P2OZ9GKRYzOaF6+18u35UeRJEmSpCEZtqBYVW/ZhmNWA6ub5buTPAhMBx4DJvfbdXIzNmw2\nBMWt+YiMJ599ktk3z2bBEwv46BEf5f2veP+QXlYzec/JnPnKMznzlWdy35P3Me/heVzz0DXMuXUO\nY0ePZfcxu7P/i/ena0zXNv88kiRJkrS1OmrqaZK9gRVVtS7JAbReWvNQVa1I8nSSGcAdwN8C/zGc\ntWx4RnFLdxQfffpRPnTjh3j8mce56A0XcdLUk7brutPHT2f6+OnMPnw29zxxD1c/dDU3PHoDx006\nbrvOK0mSJElbq10fj/EOWkFvb+DqJAuq6iTg9cCnk6wB1gNnV9WGpPYh/vTxGPMYxhfZAOw+ZnfG\njh672aD4s2U/Y/bNswnhKyd9hb59+nbY9ZPQt08fffv0MWfGnB12XkmSJEnakna99fRK4MpBxi8H\nLt/EMXcBhw5zac9LQm9X7yannl778LXMuXUO++6xLxe/+WKm/MW2vTRHkiRJkjpNR0097TQ9XT1/\ndkexqrh04aV8cf4XefU+r2bum+ayV9debapQkiRJknY8g+Jm9HT38MQfnnh+fe36tVx4x4V8977v\ncsrUU/jMsZ9h7OixbaxQkiRJknY8g+Jm9Hb1snj5YgBWPbeKc398Lrf9+jY++MoP8uHDP8yojGpz\nhZIkSZK04xkUN2PD1NPHn3mcc246hwefepALjrmA06af1u7SJEmSJGnYGBQ3o6erh7W1ltN/cDqr\n163m4jdfzGsnvbbdZUmSJEnSsDIobkZvdy8Au43ajUtOuIQDew5sc0WSJEmSNPwMiptx9L5HM+ug\nWXzg0A8wcdzEdpcjSZIkSTuFQXEzJnRP4Pyjz293GZIkSZK0U/naTkmSJEnSAAZFSZIkSdIABkVJ\nkiRJ0gAGRUmSJEnSAAZFSZIkSdIABkVJkiRJ0gAGRUmSJEnSAAZFSZIkSdIAqap21zCskqwElrS7\nDmkQE4DftbsIaRPsT3Uqe1Odyt5UJzuwqvYcygFjhquSDrKkqo5sdxHSxpLcZW+qU9mf6lT2pjqV\nvalOluSuoR7j1FNJkiRJ0gAGRUmSJEnSALtCULyk3QVIm2BvqpPZn+pU9qY6lb2pTjbk/hzxL7OR\nJEmSJA3NrnBHUZIkSZI0BAZFSZIkSdIAIzYoJjk5yZIkDyQ5r931aNeW5NIky5Is7DfWk+SGJPc3\n38e3s0btmpLsl+SHSX6Z5BdJPtKM259qqyRdSe5Mck/Tm//SjNub6ghJRif5WZIfNOv2pjpCkkeS\n3JtkwYaPxdiW/hyRQTHJaOA/gVOAQ4C/SXJIe6vSLu5rwMkbjZ0H3FRV04CbmnVpZ1sLfKyqDgFm\nAOc0f17an2q31cDxVXUY0AecnGQG9qY6x0eARf3W7U11kjdVVV+/z/Yccn+OyKAIHAU8UFUPVdVz\nwP8Cb2tzTdqFVdVPgBUbDb8NuKxZvgx4+04tSgKq6jdVNb9ZXknrHz2TsD/VZtWyqlndrfkq7E11\ngCSTgb8Evtxv2N5UJxtyf47UoDgJ+FW/9aXNmNRJJlbVb5rlx4GJ7SxGSjIVOBy4A/tTHaCZ2rcA\nWAbcUFX2pjrFF4GPA+v7jdmb6hQF3Jjk7iRnNWND7s8xw1WdpK1XVZXEz6pR2yTZA7gc+MeqejrJ\n89vsT7VLVa0D+pLsBVyZ5NCNttub2umSvBVYVlV3J3njYPvYm2qzY6vqsST7ADckWdx/49b250i9\no/gYsF+/9cnNmNRJfptkX4Dm+7I216NdVJLdaIXEb1bVFc2w/amOUVVPAT+k9ay3val2ex1wapJH\naD3edHySb2BvqkNU1WPN92XAlbQeyxtyf47UoPhTYFqS/ZO8CPhr4Ko21yRt7CrgjGb5DOD7baxF\nu6i0bh1+BVhUVf/eb5P9qbZKsndzJ5Ek3cAJwGLsTbVZVZ1fVZOraiqtf2PeXFXvxd5UB0gyLsme\nG5aBE4GFbEN/pmpk3hVPMpPW/PHRwKVVdWGbS9IuLMm3gDcCE4DfAp8Cvgd8G5gCPAq8u6o2fuGN\nNKySHAvcAtzLn561+QSt5xTtT7VNklfReuHCaFr/sf3tqvp0kl7sTXWIZurpuVX1VntTnSDJAbTu\nIkLrMcP/qaoLt6U/R2xQlCRJkiRtm5E69VSSJEmStI0MipIkSZKkAQyKkiRJkqQBDIqSJEmSpAEM\nipIkSZKkAQyKkqQXrCT/13yfmmTWDj73Jwa7VqdK8v4kX2p3HZKkkcGgKEl6waqq1zaLU4EhBcUk\nY7awy4Cg2O9aI1KS0e2uQZLUOQyKkqQXrCSrmsXPAcclWZDkn5KMTvKFJD9N8vMkf9fs/8YktyS5\nCvhlM/a9JHcn+UWSs5qxzwHdzfm+2f9aaflCkoVJ7k1yer9z/yjJd5MsTvLNJBmk5h8l+XySO5Pc\nl+S4ZnzAHcEkP2g+zJskq5pr/iLJjUmOas7zUJJT+51+v2b8/iSf6neu9zbXW5DkvzeEwua8/5bk\nHuCYHfBbIkkaIbb0v6mSJL0QnAecW1VvBWgC3++r6jVJxgK3Jbm+2ffVwKFV9XCz/oGqWpGkG/hp\nksur6rwkH66qvkGu9U6gDzgMmNAc85Nm2+HAK4BfA7cBrwNuHeQcY6rqqCQzgU8Bb9nCzzcOuLmq\n/jnJlcC/AicAhwCXAVc1+x0FHAr8oanrauAZ4HTgdVW1JsnFwHuArzfnvaOqPraF60uSdjEGRUnS\nSHQi8Kok72rWXwxMA54D7uwXEgFmJ3lHs7xfs9/yzZz7WOBbVbUO+G2SHwOvAZ5uzr0UIMkCWlNi\nBwuKVzTf72722ZLngGub5XuB1U3ou3ej42+oquXN9a9oal0LHEErOAJ0A8ua/dcBl2/F9SVJuxiD\noiRpJArwD1V13YDB1lTOZzZafwtwTFX9IcmPgK7tuO7qfsvr2PTfs6sH2WctAx8J6V/HmqqqZnn9\nhuOrav1Gz1oWAxWtX4vLqur8Qep4tgm8kiQN4DOKkqSRYCWwZ7/164C/T7IbQJLpScYNctyLgSeb\nkHgQMKPftjUbjt/ILcDpzXOQewOvB+7cAT/DI0BfklFJ9qM1jXSoTkjS00yjfTut6a83Ae9Ksg9A\ns/2lO6BeSdII5h1FSdJI8HNgXfNSlq8Bc2lNyZzfvFDmCVrBaWPXAmcnWQQsAW7vt+0S4OdJ5lfV\ne/qNX0nrxS/30Lpj9/GqerwJmtvjNuBhWi/ZWQTM34Zz3ElrKulk4BtVdRdAkk8C1ycZBawBzgEe\n3c56JUkjWP40k0WSJEmSJKeeSpIkSZI2YlCUJEmSJA1gUJQkSZIkDWBQlCRJkiQNYFCUJEmSJA1g\nUJQkSZIkDWBQlCRJkiQN8P9ywTmk5sLJZQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f47cb6c65f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outgraph3 = GN_Q_0.plot(x=GN_Q_0.index,y=['phi','theta','psi'],\n",
    "                        title=\"Gauss Newton Output for Roll, Pitch, Yaw in degrees\",\n",
    "                        figsize=(15.0,4.0),legend=True)\n",
    "outgraph3.set_xlabel(\"iteration number\")\n",
    "outgraph3.set_ylabel(\"phi, theta, psi in degrees\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "88.47488584474885"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## X 50degrees \n",
    "\n",
    " Timestamp        Ax        Ay        Az        Gx        Gy  \\\n",
    "1125  1494779731809  0.344765 -0.134075  9.710882 -0.001065  0.004261   \n",
    "1126  1494779731830  0.344765 -0.134075  9.634268 -0.001065  0.003196   \n",
    "1127  1494779731853  0.344765 -0.134075  9.634268 -0.006392  0.001065   \n",
    "1128  1494779731874  0.344765 -0.134075  9.634268 -0.006392  0.001065   \n",
    "1129  1494779731895  0.363919 -0.114922  9.595961 -0.002131  0.004261   \n",
    "\n",
    "            Gz   MFx   MFy   MFz  \n",
    "1125  0.001065 -9.00  6.75 -29.5  \n",
    "1126  0.002131 -8.25  6.75 -29.5  \n",
    "1127  0.002131 -8.25  6.75 -29.5  \n",
    "1128  0.002131 -8.25  6.75 -29.5  \n",
    "1129 -0.001065 -9.00  6.25 -30.0  \n",
    "Timestamp    1.494780e+12\n",
    "Ax           3.498182e-01\n",
    "Ay          -1.278746e-01\n",
    "Az           9.645478e+00\n",
    "Gx          -1.081219e-03\n",
    "Gy           3.489109e-03\n",
    "Gz           2.149552e-03\n",
    "MFx         -8.154090e+00\n",
    "MFy          6.280098e+00\n",
    "MFz         -3.016979e+01\n",
    "dtype: float64\n",
    "    \n",
    "\n",
    "## at 0 degrees\n",
    "\n",
    "          Timestamp        Ax        Ay        Az        Gx        Gy  \\\n",
    "1125  1494275017864  0.402226 -0.210690  9.595961 -0.004261  0.002131   \n",
    "1126  1494275017886  0.383072 -0.191536  9.672575 -0.004261  0.002131   \n",
    "1127  1494275017909  0.402226 -0.191536  9.576807  0.002131  0.003196   \n",
    "1128  1494275017930  0.383072 -0.191536  9.672575 -0.003196  0.001065   \n",
    "1129  1494275017952  0.421380 -0.191536  9.615114 -0.004261 -0.001065   \n",
    "\n",
    "            Gz   MFx    MFy    MFz  \n",
    "1125  0.002131 -2.75  22.25 -39.75  \n",
    "1126  0.002131 -2.25  21.75 -39.25  \n",
    "1127  0.001065 -2.25  21.75 -39.25  \n",
    "1128  0.001065 -1.75  21.75 -39.00  \n",
    "1129  0.004261 -1.75  21.75 -39.00  \n",
    "Timestamp    1.494275e+12\n",
    "Ax           4.030215e-01\n",
    "Ay          -1.938762e-01\n",
    "Az           9.632899e+00\n",
    "Gx          -1.060709e-03\n",
    "Gy           3.092325e-03\n",
    "Gz           1.810039e-03\n",
    "MFx         -2.680208e+00\n",
    "MFy          2.209064e+01\n",
    "MFz         -3.946090e+01\n",
    "dtype: float64\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.525114155251142"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "112*46/219"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
